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Matching statistic: St000642
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St000642: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000642: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> ([(0,1)],2)
=> 3
[1,1,0,0]
=> ([],2)
=> 2
[1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> 4
[1,0,1,1,0,0]
=> ([(0,2),(1,2)],3)
=> 2
[1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> 2
[1,1,0,1,0,0]
=> ([(1,2)],3)
=> 6
[1,1,1,0,0,0]
=> ([],3)
=> 2
[1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 5
[1,0,1,0,1,1,0,0]
=> ([(0,3),(1,3),(3,2)],4)
=> 2
[1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> 7
[1,0,1,1,1,0,0,0]
=> ([(0,3),(1,3),(2,3)],4)
=> 2
[1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> 2
[1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> 7
[1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3)],4)
=> 3
[1,1,0,1,1,0,0,0]
=> ([(1,3),(2,3)],4)
=> 2
[1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3)],4)
=> 2
[1,1,1,0,0,1,0,0]
=> ([(1,2),(1,3)],4)
=> 2
[1,1,1,0,1,0,0,0]
=> ([(2,3)],4)
=> 6
[1,1,1,1,0,0,0,0]
=> ([],4)
=> 2
[1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6
[1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 8
[1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 8
[1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> 6
[1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> 8
[1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 4
[1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> 10
[1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> 3
[1,1,0,1,1,1,0,0,0,0]
=> ([(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,0,0,1,0,1,0]
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> 2
Description
The size of the smallest orbit of antichains under Panyushev complementation.
Matching statistic: St001239
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001239: Dyck paths ⟶ ℤResult quality: 18% ●values known / values provided: 68%●distinct values known / distinct values provided: 18%
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001239: Dyck paths ⟶ ℤResult quality: 18% ●values known / values provided: 68%●distinct values known / distinct values provided: 18%
Values
[1,0,1,0]
=> [[1,1],[]]
=> []
=> []
=> ? ∊ {2,3}
[1,1,0,0]
=> [[2],[]]
=> []
=> []
=> ? ∊ {2,3}
[1,0,1,0,1,0]
=> [[1,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,4,6}
[1,0,1,1,0,0]
=> [[2,1],[]]
=> []
=> []
=> ? ∊ {2,2,4,6}
[1,1,0,0,1,0]
=> [[2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [[3],[]]
=> []
=> []
=> ? ∊ {2,2,4,6}
[1,1,1,0,0,0]
=> [[2,2],[]]
=> []
=> []
=> ? ∊ {2,2,4,6}
[1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [[4],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [[4,2],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [[4,3],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [[4,4],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> []
=> []
=> ? ∊ {2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [[4,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [[4,4,1],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [[5,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> [1]
=> [1,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [[4,2,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [[4,3,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [[4,4,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [[6],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [[5,2],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [[4,2,2],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [[3,2,2,2],[]]
=> []
=> []
=> ? ∊ {4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
Description
The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra.
Matching statistic: St000259
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [2,1] => ([(0,2),(1,2)],3)
=> 2
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [3] => ([],3)
=> ? = 3
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {4,6}
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [4] => ([],4)
=> ? ∊ {4,6}
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {3,5,6,7,7}
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ? ∊ {3,5,6,7,7}
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,5,6,7,7}
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [5] => ([],5)
=> ? ∊ {3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,4] => ([(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [6] => ([],6)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [2,5] => ([(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [3,4] => ([(3,6),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St001198
(load all 54 compositions to match this statistic)
(load all 54 compositions to match this statistic)
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [1,2] => [1,2] => [1,0,1,0]
=> 2
[1,1,0,0]
=> [2,1] => [2,1] => [1,1,0,0]
=> ? = 3
[1,0,1,0,1,0]
=> [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0]
=> [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,0]
=> [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
=> ? ∊ {4,6}
[1,1,1,0,0,0]
=> [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? ∊ {4,6}
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,0,1,1,0,0,0]
=> [2,4,3,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,0,1,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,0,1,0]
=> [4,2,3,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,1,0,0,0,0]
=> [5,3,4,2,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,5,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,4,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,6,4,5,1] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,3,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,5,3,4,6,1] => [6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,6,3,4,5,1] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,6,3,5,4,1] => [6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,4,3,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,6,4,3,5,1] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,6,4,5,3,1] => [6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,2,4,5,6,1] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,2,4,6,5,1] => [6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,5,4,6,1] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,6,4,5,1] => [6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,2,3,5,6,1] => [6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,2,3,6,5,1] => [6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,2,3,4,6,1] => [6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [6,2,3,4,5,1] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [6,2,3,5,4,1] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,4,3,6,1] => [6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [6,2,4,3,5,1] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [6,2,4,5,3,1] => [6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [6,2,5,4,3,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001206
(load all 54 compositions to match this statistic)
(load all 54 compositions to match this statistic)
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Mp00066: Permutations —inverse⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [1,2] => [1,2] => [1,0,1,0]
=> 2
[1,1,0,0]
=> [2,1] => [2,1] => [1,1,0,0]
=> ? = 3
[1,0,1,0,1,0]
=> [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> 2
[1,0,1,1,0,0]
=> [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> 2
[1,1,0,0,1,0]
=> [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> 2
[1,1,0,1,0,0]
=> [2,3,1] => [3,1,2] => [1,1,1,0,0,0]
=> ? ∊ {4,6}
[1,1,1,0,0,0]
=> [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
=> ? ∊ {4,6}
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> 2
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,0,1,1,0,0,0]
=> [2,4,3,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,0,1,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,2,1,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,0,1,0]
=> [4,2,3,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,1,0,0,0,0]
=> [5,3,4,2,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,5,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,4,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,6,4,5,1] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,3,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,5,3,4,6,1] => [6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,6,3,4,5,1] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,6,3,5,4,1] => [6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,4,3,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,6,4,3,5,1] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,6,4,5,3,1] => [6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,2,4,5,6,1] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,2,4,6,5,1] => [6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,5,4,6,1] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,6,4,5,1] => [6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,2,3,5,6,1] => [6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,2,3,6,5,1] => [6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,2,3,4,6,1] => [6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [6,2,3,4,5,1] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [6,2,3,5,4,1] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,4,3,6,1] => [6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [6,2,4,3,5,1] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [6,2,4,5,3,1] => [6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [6,2,5,4,3,1] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
Description
The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.
Matching statistic: St001704
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001704: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001704: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [1,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 2
[1,1,0,0]
=> [2] => ([],2)
=> ([],1)
=> ? = 3
[1,0,1,0,1,0]
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,0,0]
=> [1,2] => ([(1,2)],3)
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,0]
=> [2,1] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,0]
=> [3] => ([],3)
=> ([],1)
=> ? ∊ {4,6}
[1,1,1,0,0,0]
=> [3] => ([],3)
=> ([],1)
=> ? ∊ {4,6}
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,0]
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,0,0,1,0]
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,0,1,0,0]
=> [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,0,1,1,1,0,0,0]
=> [1,3] => ([(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,0,1,0]
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,1,0,0,1,1,0,0]
=> [2,2] => ([(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,0,1,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,1,0,0]
=> [4] => ([],4)
=> ([],1)
=> ? ∊ {3,5,6,7,7}
[1,1,0,1,1,0,0,0]
=> [4] => ([],4)
=> ([],1)
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,0,0,1,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,1,1,0,0,1,0,0]
=> [4] => ([],4)
=> ([],1)
=> ? ∊ {3,5,6,7,7}
[1,1,1,0,1,0,0,0]
=> [4] => ([],4)
=> ([],1)
=> ? ∊ {3,5,6,7,7}
[1,1,1,1,0,0,0,0]
=> [4] => ([],4)
=> ([],1)
=> ? ∊ {3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,1,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,1,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,1,0,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,1,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,1,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,1,0,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,1,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,1,0,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,1,0,0,0,0,0]
=> [5] => ([],5)
=> ([],1)
=> ? ∊ {2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [6] => ([],6)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
Description
The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph.
The deck of a graph is the multiset of induced subgraphs obtained by deleting a single vertex.
The graph reconstruction conjecture states that the deck of a graph with at least three vertices determines the graph.
This statistic is only defined for graphs with at least two vertices, because there is only a single graph of the given size otherwise.
Matching statistic: St000260
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 67%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [3,1,2] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {2,3}
[1,1,0,0]
=> [2,3,1] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {2,3}
[1,0,1,0,1,0]
=> [4,1,2,3] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,4,6}
[1,0,1,1,0,0]
=> [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,0,1,0]
=> [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,0]
=> [4,3,1,2] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {2,4,6}
[1,1,1,0,0,0]
=> [2,3,4,1] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,4,6}
[1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,3,5,6,7,7}
[1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,3,5,6,7,7}
[1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,3,5,6,7,7}
[1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,3,5,6,7,7}
[1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? ∊ {2,3,5,6,7,7}
[1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => [4,6,3,2,1,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => [5,3,6,2,1,4] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => [3,6,5,2,1,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => [5,4,2,6,1,3] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => [4,6,2,5,1,3] => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => [5,3,2,4,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => [3,6,2,4,1,5] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => [5,2,6,4,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => [4,2,5,6,1,3] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => [3,2,5,4,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => [2,6,5,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => [5,4,3,1,6,2] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => [4,6,3,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => [5,3,6,1,4,2] => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => [4,3,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => [3,6,5,1,4,2] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => [5,4,2,1,3,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => [4,6,2,1,3,5] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => [5,3,2,1,4,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => [3,6,2,1,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => [5,2,6,1,3,4] => ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> 2
[1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => [4,2,5,1,3,6] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => [3,2,5,1,4,6] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => [2,6,5,1,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => [5,4,1,6,3,2] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => [4,6,1,5,3,2] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => [5,3,1,4,6,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => [4,3,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => [3,6,1,4,5,2] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => [5,2,1,4,3,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => [4,2,1,5,3,6] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => [2,6,1,4,3,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => [5,1,6,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => [4,1,5,6,3,2] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => [3,1,5,4,6,2] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [6,3,4,5,1,2] => [2,1,5,4,3,6] => ([(1,2),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,1,2,3,4,7,5] => [5,7,4,3,2,1,6] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,1,2,3,7,4,6] => [6,4,7,3,2,1,5] => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [7,1,2,3,6,4,5] => [5,4,6,3,2,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [5,1,2,3,6,7,4] => [4,7,6,3,2,1,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [4,1,2,7,3,5,6] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,1,2,6,3,7,5] => [5,7,3,6,2,1,4] => ([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [7,1,2,5,3,4,6] => [6,4,3,5,2,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [7,1,2,6,3,4,5] => [5,4,3,6,2,1,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [6,1,2,5,3,7,4] => [4,7,3,5,2,1,6] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [4,1,2,5,7,3,6] => [6,3,7,5,2,1,4] => ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,1,2,7,6,3,5] => [5,3,6,7,2,1,4] => ([(0,2),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [7,1,2,5,6,3,4] => [4,3,6,5,2,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,1,2,5,6,7,3] => [3,7,6,5,2,1,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [3,1,7,2,4,5,6] => [6,5,4,2,7,1,3] => ([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [3,1,6,2,4,7,5] => [5,7,4,2,6,1,3] => ([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [3,1,5,2,7,4,6] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [3,1,7,2,6,4,5] => [5,4,6,2,7,1,3] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [7,1,4,2,3,5,6] => [6,5,3,2,4,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [7,1,5,2,3,4,6] => [6,4,3,2,5,1,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [7,1,4,2,6,3,5] => [5,3,6,2,4,1,7] => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [7,1,5,2,6,3,4] => [4,3,6,2,5,1,7] => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [7,1,4,5,2,3,6] => [6,3,2,5,4,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [7,1,4,6,2,3,5] => [5,3,2,6,4,1,7] => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [7,1,6,5,2,3,4] => [4,3,2,5,6,1,7] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => [3,2,6,5,4,1,7] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [7,3,1,2,4,5,6] => [6,5,4,2,1,3,7] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [7,3,1,2,6,4,5] => [5,4,6,2,1,3,7] => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [7,4,1,2,3,5,6] => [6,5,3,2,1,4,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [7,6,1,2,3,4,5] => [5,4,3,2,1,6,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [7,4,1,2,6,3,5] => [5,3,6,2,1,4,7] => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [7,3,1,5,2,4,6] => [6,4,2,5,1,3,7] => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [7,3,1,6,2,4,5] => [5,4,2,6,1,3,7] => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [7,4,1,5,2,3,6] => [6,3,2,5,1,4,7] => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [7,4,1,6,2,3,5] => [5,3,2,6,1,4,7] => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [6,7,1,5,2,3,4] => [4,3,2,5,1,7,6] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [7,3,1,5,6,2,4] => [4,2,6,5,1,3,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St001060
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 41%●distinct values known / distinct values provided: 9%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 41%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {2,3}
[1,1,0,0]
=> [1,2] => ([],2)
=> ([],1)
=> ? ∊ {2,3}
[1,0,1,0,1,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,4,6}
[1,0,1,1,0,0]
=> [2,1,3] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,4,6}
[1,1,0,0,1,0]
=> [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,4,6}
[1,1,0,1,0,0]
=> [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,4,6}
[1,1,1,0,0,0]
=> [1,2,3] => ([],3)
=> ([],1)
=> ? ∊ {2,2,2,4,6}
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,1,0,1,0,0,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 2
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> 2
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [3,1,4,5,2,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> 2
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> 2
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 2
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Matching statistic: St001330
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 55%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 55%
Values
[1,0,1,0]
=> [1,1] => ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 3
[1,1,0,0]
=> [2] => ([],2)
=> ([(0,2),(1,2)],3)
=> 2
[1,0,1,0,1,0]
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0]
=> [1,2] => ([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,6}
[1,1,0,0,1,0]
=> [2,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {2,6}
[1,1,0,1,0,0]
=> [3] => ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 2
[1,1,1,0,0,0]
=> [3] => ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 2
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5
[1,0,1,0,1,1,0,0]
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,0,1,1,0,0,1,0]
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,0,1,1,0,1,0,0]
=> [1,3] => ([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,0,1,1,1,0,0,0]
=> [1,3] => ([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,1,0,0,1,0,1,0]
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,1,0,0,1,1,0,0]
=> [2,2] => ([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,1,0,1,0,0,1,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,1,0,1,0,1,0,0]
=> [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,0,1,1,0,0,0]
=> [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,0,0,1,0]
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,2,3,6,7,7}
[1,1,1,0,0,1,0,0]
=> [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,0,1,0,0,0]
=> [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,1,1,1,0,0,0,0]
=> [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => ([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,0,1,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,1,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,0,1,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,0,0,1,1,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,1,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,1,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,0,1,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,9,9,9,9,11,11,11,18,18}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St001545
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001545: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 29%●distinct values known / distinct values provided: 9%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001545: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 29%●distinct values known / distinct values provided: 9%
Values
[1,0,1,0]
=> [2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> 2
[1,1,0,0]
=> [1,2] => ([],2)
=> ([],1)
=> ? = 3
[1,0,1,0,1,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 2
[1,0,1,1,0,0]
=> [2,1,3] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,4,6}
[1,1,0,0,1,0]
=> [1,3,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> ? ∊ {2,4,6}
[1,1,0,1,0,0]
=> [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> 2
[1,1,1,0,0,0]
=> [1,2,3] => ([],3)
=> ([],1)
=> ? ∊ {2,4,6}
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 2
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => ([(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => ([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,1,1,0,1,0,0,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> 2
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ([],1)
=> ? ∊ {2,2,2,2,3,5,6,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,0,1,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ([],1)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,4,4,6,6,6,6,6,8,8,8,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,4),(2,3),(3,4)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6)
=> ([(1,4),(2,3)],5)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ([(0,3),(1,2)],4)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => ([(3,5),(4,5)],6)
=> ([(1,2)],3)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,9,9,9,9,11,11,11,18,18}
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> 2
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,0,0,1,0,1,0]
=> [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2),(2,3)],4)
=> 2
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
Description
The second Elser number of a connected graph.
For a connected graph $G$ the $k$-th Elser number is
$$
els_k(G) = (-1)^{|V(G)|+1} \sum_N (-1)^{|E(N)|} |V(N)|^k
$$
where the sum is over all nuclei of $G$, that is, the connected subgraphs of $G$ whose vertex set is a vertex cover of $G$.
It is clear that this number is even. It was shown in [1] that it is non-negative.
The following 6 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
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