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Your data matches 11 different statistics following compositions of up to 3 maps.
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Matching statistic: St001137
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(load all 5 compositions to match this statistic)
St001137: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 0
[1,0,1,0]
=> 0
[1,1,0,0]
=> 0
[1,0,1,0,1,0]
=> 1
[1,0,1,1,0,0]
=> 0
[1,1,0,0,1,0]
=> 0
[1,1,0,1,0,0]
=> 0
[1,1,1,0,0,0]
=> 0
[1,0,1,0,1,0,1,0]
=> 0
[1,0,1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0,1,0]
=> 0
[1,0,1,1,0,1,0,0]
=> 0
[1,0,1,1,1,0,0,0]
=> 0
[1,1,0,0,1,0,1,0]
=> 1
[1,1,0,0,1,1,0,0]
=> 0
[1,1,0,1,0,0,1,0]
=> 0
[1,1,0,1,0,1,0,0]
=> 1
[1,1,0,1,1,0,0,0]
=> 0
[1,1,1,0,0,0,1,0]
=> 0
[1,1,1,0,0,1,0,0]
=> 0
[1,1,1,0,1,0,0,0]
=> 0
[1,1,1,1,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> 0
[1,0,1,0,1,0,1,1,0,0]
=> 0
[1,0,1,0,1,1,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> 0
[1,0,1,0,1,1,1,0,0,0]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> 0
[1,0,1,1,0,1,0,0,1,0]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> 0
[1,1,0,0,1,0,1,1,0,0]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> 0
[1,1,0,1,0,0,1,1,0,0]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> 0
[1,1,0,1,0,1,0,1,0,0]
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> 0
[1,1,0,1,1,1,0,0,0,0]
=> 0
Description
Number of simple modules that are 3-regular in the corresponding Nakayama algebra.
Matching statistic: St001719
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [1,0]
=> ([],1)
=> ([(0,1)],2)
=> 1 = 0 + 1
[1,0,1,0]
=> [1,1,0,0]
=> ([],2)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[1,1,0,0]
=> [1,0,1,0]
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> ([(1,2)],3)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 1 + 1
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1 = 0 + 1
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1 = 0 + 1
[1,1,0,1,0,0]
=> [1,1,1,0,0,0]
=> ([],3)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> 1 = 0 + 1
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> ([(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 2 = 1 + 1
[1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> ([(1,2),(1,3)],4)
=> ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
=> ? = 0 + 1
[1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0]
=> ([],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 1 + 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3)],4)
=> ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 1 = 0 + 1
[1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
=> 1 = 0 + 1
[1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> ([(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
=> ? = 0 + 1
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> 1 = 0 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> ([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12)
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> ([(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> 2 = 1 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> 1 = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12)
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> ([(1,2),(1,3),(1,4)],5)
=> ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> ([(3,4)],5)
=> ?
=> ? = 2 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
=> ? = 1 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
=> ? = 0 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> ([(2,3),(2,4)],5)
=> ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> 2 = 1 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11)
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
=> ? = 1 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
=> ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
=> ? = 0 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> ([(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
=> ? = 0 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ([],5)
=> ?
=> ? = 1 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
=> ? = 0 + 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
=> ? = 0 + 1
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ([(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
=> ? = 0 + 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ([(0,5),(0,6),(1,11),(2,8),(3,7),(4,10),(5,9),(6,1),(6,9),(8,7),(9,4),(9,11),(10,3),(10,8),(11,2),(11,10)],12)
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ([(0,6),(1,8),(2,9),(3,10),(4,7),(5,3),(5,9),(6,2),(6,5),(7,8),(9,4),(9,10),(10,1),(10,7)],11)
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,4),(0,5),(1,8),(2,10),(3,7),(4,9),(5,9),(6,3),(6,10),(7,8),(9,2),(9,6),(10,1),(10,7)],11)
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(0,6),(1,10),(2,12),(3,7),(4,9),(4,11),(5,8),(5,11),(6,8),(6,9),(7,10),(8,13),(9,13),(11,2),(11,13),(12,1),(12,7),(13,3),(13,12)],14)
=> ? = 0 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,5),(1,8),(2,9),(3,7),(4,3),(4,9),(5,6),(6,2),(6,4),(7,8),(9,1),(9,7)],10)
=> ? = 0 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ([(0,4),(0,6),(1,10),(2,9),(3,8),(4,7),(5,2),(5,8),(6,1),(6,7),(7,10),(8,9),(10,3),(10,5)],11)
=> ? = 2 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ([(0,6),(1,9),(2,9),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,8),(9,4),(9,5)],10)
=> ? = 1 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(0,6),(1,10),(2,9),(3,8),(3,11),(4,8),(4,12),(5,7),(6,3),(6,4),(6,7),(7,11),(7,12),(8,13),(9,10),(11,13),(12,2),(12,13),(13,1),(13,9)],14)
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,14),(3,8),(3,9),(3,10),(4,10),(4,12),(4,13),(5,9),(5,11),(5,13),(6,8),(6,11),(6,12),(8,15),(8,16),(9,15),(9,17),(10,16),(10,17),(11,15),(11,18),(12,16),(12,18),(13,17),(13,18),(14,7),(15,19),(16,19),(17,19),(18,2),(18,19),(19,1),(19,14)],20)
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,6),(1,10),(2,9),(3,8),(3,11),(4,7),(4,11),(5,7),(5,8),(6,3),(6,4),(6,5),(7,12),(8,12),(9,10),(11,2),(11,12),(12,1),(12,9)],13)
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ([(0,3),(0,4),(1,9),(2,8),(3,7),(4,7),(5,1),(5,8),(6,2),(6,5),(7,6),(8,9)],10)
=> ? = 1 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ([(0,3),(0,4),(0,5),(1,11),(2,7),(3,9),(3,10),(4,8),(4,10),(5,8),(5,9),(6,1),(6,7),(7,11),(8,12),(9,12),(10,12),(12,2),(12,6)],13)
=> ? = 1 + 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,9),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,2),(14,15),(15,1),(15,11)],16)
=> ? = 0 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 1 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ([(0,5),(0,6),(1,10),(2,7),(3,7),(4,8),(5,9),(6,4),(6,9),(8,10),(9,1),(9,8),(10,2),(10,3)],11)
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> ([(0,6),(1,9),(2,7),(3,7),(4,8),(5,1),(5,8),(6,4),(6,5),(8,9),(9,2),(9,3)],10)
=> ? = 1 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(0,6),(1,11),(2,7),(3,7),(4,9),(4,10),(5,8),(5,10),(6,8),(6,9),(8,12),(9,12),(10,1),(10,12),(11,2),(11,3),(12,11)],13)
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> ([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)
=> 1 = 0 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
=> ([(0,5),(0,6),(1,8),(1,10),(2,8),(2,11),(3,9),(4,7),(5,12),(6,4),(6,12),(7,10),(7,11),(8,13),(10,13),(11,3),(11,13),(12,1),(12,2),(12,7),(13,9)],14)
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> ([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9)
=> 1 = 0 + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> 1 = 0 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
=> 2 = 1 + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)
=> 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> ([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9)
=> 1 = 0 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
=> 2 = 1 + 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> ([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
=> 2 = 1 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
=> 1 = 0 + 1
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
=> 1 = 0 + 1
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
=> 1 = 0 + 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
=> 1 = 0 + 1
Description
The number of shortest chains of small intervals from the bottom to the top in a lattice.
An interval $[a, b]$ in a lattice is small if $b$ is a join of elements covering $a$.
Matching statistic: St001846
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [1,0]
=> [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0
[1,0,1,0]
=> [1,1,0,0]
=> [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 0
[1,1,0,0]
=> [1,0,1,0]
=> [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 0
[1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> 1
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 0
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 0
[1,1,0,1,0,0]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 0
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 0
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ? = 0
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0
[1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0
[1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? = 1
[1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0
[1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? = 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0
[1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0
[1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0
[1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ? = 0
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? = 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,13),(3,12),(4,11),(5,11),(5,14),(6,12),(6,14),(8,10),(9,10),(10,7),(11,8),(12,9),(13,7),(14,8),(14,9)],15)
=> ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(3,8),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,10),(5,11),(6,7),(6,9),(7,12),(8,11),(9,12),(11,9),(12,10)],13)
=> ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? = 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(3,8),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
=> ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,10),(6,11),(7,11),(8,12),(9,12),(11,8),(11,9),(12,10)],13)
=> ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [6,3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,9),(4,12),(5,12),(6,10),(6,11),(8,7),(9,7),(10,13),(11,13),(12,8),(13,8),(13,9)],14)
=> ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,10),(5,11),(6,7),(6,9),(7,12),(8,11),(9,12),(11,9),(12,10)],13)
=> ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,13),(3,7),(4,13),(4,16),(5,14),(5,17),(6,16),(6,17),(8,12),(9,12),(10,8),(11,9),(12,7),(13,10),(14,11),(15,8),(15,9),(16,10),(16,15),(17,11),(17,15)],18)
=> ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,10),(11,9)],12)
=> ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? = 0
[1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,10),(11,9)],12)
=> ? = 0
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,13),(3,12),(4,13),(4,14),(5,11),(5,15),(6,12),(6,15),(8,11),(9,7),(10,7),(11,9),(12,10),(13,8),(14,8),(15,9),(15,10)],16)
=> ? = 0
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,13),(3,7),(4,13),(4,16),(5,14),(5,17),(6,16),(6,17),(8,12),(9,12),(10,8),(11,9),(12,7),(13,10),(14,11),(15,8),(15,9),(16,10),(16,15),(17,11),(17,15)],18)
=> ? = 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [7,6,1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,17),(2,16),(3,15),(4,14),(4,17),(5,15),(5,19),(6,16),(6,20),(7,19),(7,20),(9,14),(10,9),(11,9),(12,10),(13,11),(14,8),(15,12),(16,13),(17,8),(18,10),(18,11),(19,12),(19,18),(20,13),(20,18)],21)
=> ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [5,7,1,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,14),(2,14),(3,14),(4,9),(5,8),(6,8),(6,10),(7,9),(7,10),(8,11),(9,12),(10,11),(10,12),(11,13),(12,13),(13,14)],15)
=> ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [6,4,1,2,3,7,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(2,12),(3,12),(4,12),(5,9),(6,8),(7,8),(7,9),(8,11),(9,11),(10,12),(11,10)],13)
=> ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [5,6,1,2,3,7,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,12),(2,12),(3,9),(4,8),(5,10),(6,10),(7,8),(7,9),(8,11),(9,11),(10,12),(11,12)],13)
=> ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [7,4,1,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,15),(2,14),(3,13),(4,12),(5,8),(6,14),(6,15),(7,11),(7,13),(9,12),(10,8),(11,10),(12,11),(13,10),(14,9),(15,9)],16)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [7,3,1,2,6,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,9),(4,9),(5,12),(6,11),(7,10),(8,11),(9,12),(11,13),(12,13),(13,10)],14)
=> ? = 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,1,2,7,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,9),(2,10),(3,10),(4,10),(5,10),(6,8),(7,8),(8,9),(9,10)],11)
=> ? = 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [7,4,1,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(2,10),(3,10),(4,10),(5,8),(6,8),(7,9),(8,10),(10,9)],11)
=> ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [5,4,1,2,6,7,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(2,10),(3,10),(4,9),(5,9),(6,8),(7,8),(8,11),(9,11),(10,11)],12)
=> ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [5,4,1,2,7,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(2,10),(3,10),(4,9),(5,9),(6,8),(7,8),(8,10),(9,10)],11)
=> ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [6,3,1,2,4,7,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,11),(4,11),(5,11),(6,9),(7,10),(8,10),(9,11),(10,9)],12)
=> ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [5,3,1,2,6,7,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(2,11),(3,11),(4,8),(5,8),(6,9),(7,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [5,7,1,2,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(2,10),(3,10),(4,9),(5,9),(6,8),(7,8),(8,10),(9,10)],11)
=> ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [7,3,1,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,14),(2,15),(3,15),(4,13),(5,8),(6,14),(6,16),(7,12),(7,16),(9,11),(10,11),(11,8),(12,10),(13,12),(14,9),(15,13),(16,9),(16,10)],17)
=> ? = 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,7,1,6,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,10),(2,12),(3,12),(4,12),(5,9),(6,8),(7,8),(7,9),(8,11),(9,11),(10,12),(11,10)],13)
=> ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,7,1,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,11),(4,11),(5,11),(6,9),(7,10),(8,10),(9,11),(10,9)],12)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,4,1,6,3,7,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,6,1,5,3,7,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [6,3,1,5,2,7,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,5,1,3,7,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,4,1,5,7,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [6,4,1,5,2,7,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [3,1,5,2,7,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,1,4,2,7,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [3,1,6,2,4,7,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> [2,6,4,1,3,7,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [2,7,4,1,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,7,4,6,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [3,1,7,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [3,1,4,6,2,7,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0
Description
The number of elements which do not have a complement in the lattice.
A complement of an element $x$ in a lattice is an element $y$ such that the meet of $x$ and $y$ is the bottom element and their join is the top element.
Matching statistic: St001964
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> ([(0,1)],2)
=> 0
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 0
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ? = 0
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ? = 0
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ? = 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ? = 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 0
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[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]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
=> ? = 0
[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]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
=> ? = 0
[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]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> ([(0,6),(1,11),(2,8),(3,9),(4,3),(4,7),(5,1),(5,7),(6,4),(6,5),(7,9),(7,11),(9,10),(10,8),(11,2),(11,10)],12)
=> ? = 0
[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]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12)
=> ? = 0
[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]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11)
=> ? = 0
[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]
=> [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> ([(0,6),(1,11),(2,8),(3,9),(4,3),(4,7),(5,1),(5,7),(6,4),(6,5),(7,9),(7,11),(9,10),(10,8),(11,2),(11,10)],12)
=> ? = 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]
=> [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> ([(0,6),(1,9),(2,7),(3,8),(4,3),(4,10),(5,4),(5,7),(6,2),(6,5),(7,10),(8,9),(10,1),(10,8)],11)
=> ? = 1
[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]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> ([(0,6),(1,8),(2,9),(3,10),(4,7),(5,3),(5,9),(6,2),(6,5),(7,8),(9,4),(9,10),(10,1),(10,7)],11)
=> ? = 0
[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]
=> [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> ([(0,6),(1,11),(2,8),(3,9),(4,5),(4,11),(5,3),(5,7),(6,1),(6,4),(7,8),(7,9),(8,10),(9,10),(11,2),(11,7)],12)
=> ? = 0
[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]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
=> ? = 0
[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]
=> [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> ([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
=> ? = 1
[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]
=> [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> ([(0,6),(1,8),(2,9),(3,10),(4,7),(5,3),(5,9),(6,2),(6,5),(7,8),(9,4),(9,10),(10,1),(10,7)],11)
=> ? = 1
[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]
=> [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> ([(0,6),(1,9),(2,7),(3,8),(4,3),(4,10),(5,4),(5,7),(6,2),(6,5),(7,10),(8,9),(10,1),(10,8)],11)
=> ? = 0
[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]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11)
=> ? = 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> ([(0,6),(2,9),(3,8),(4,3),(4,7),(5,2),(5,7),(6,4),(6,5),(7,8),(7,9),(8,10),(9,10),(10,1)],11)
=> ? = 0
[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]
=> [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> ([(0,6),(2,9),(3,7),(4,2),(4,8),(5,4),(5,7),(6,3),(6,5),(7,8),(8,9),(9,1)],10)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 0
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 0
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St001095
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St001095: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St001095: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> ([(0,1)],2)
=> 0
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,1,0,0]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 0
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 0
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 0
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
=> ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 0
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
=> ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
=> ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
=> ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
=> ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[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]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ? = 0
[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]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13)
=> ? = 0
[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]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> ([(0,4),(0,6),(2,8),(3,9),(4,10),(5,3),(5,7),(6,5),(6,10),(7,8),(7,9),(8,11),(9,11),(10,2),(10,7),(11,1)],12)
=> ? = 0
[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]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> ([(0,5),(0,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,7),(6,4),(6,7),(7,8),(7,10),(8,11),(9,12),(10,9),(10,11),(11,12),(12,1)],13)
=> ? = 0
[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]
=> [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
=> ? = 0
[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]
=> [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> ([(0,4),(0,6),(1,12),(2,8),(3,10),(4,11),(5,1),(5,7),(6,5),(6,11),(7,10),(7,12),(9,8),(10,9),(11,3),(11,7),(12,2),(12,9)],13)
=> ? = 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]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10)
=> ? = 1
[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]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> ([(0,4),(0,6),(1,12),(2,8),(3,10),(4,11),(5,3),(5,7),(6,5),(6,11),(7,10),(7,12),(9,8),(10,9),(11,1),(11,7),(12,2),(12,9)],13)
=> ? = 0
[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]
=> [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=> ([(0,5),(0,6),(1,11),(2,4),(2,13),(3,7),(4,10),(5,1),(5,12),(6,2),(6,12),(8,9),(9,7),(10,3),(10,9),(11,8),(12,11),(12,13),(13,8),(13,10)],14)
=> ? = 0
[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]
=> [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
=> ? = 0
[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]
=> [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
=> ? = 1
[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]
=> [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10)
=> ? = 1
[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]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
=> ? = 0
[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]
=> [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=> ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
=> ? = 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> ([(0,6),(1,11),(2,8),(3,9),(4,3),(4,7),(5,1),(5,7),(6,4),(6,5),(7,9),(7,11),(9,10),(10,8),(11,2),(11,10)],12)
=> ? = 0
[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]
=> [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
=> ? = 1
Description
The number of non-isomorphic posets with precisely one further covering relation.
Matching statistic: St001207
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> []
=> []
=> [1] => ? = 0 + 2
[1,0,1,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
[1,1,0,0]
=> []
=> []
=> [1] => ? = 0 + 2
[1,0,1,0,1,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,0,1,1,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,1,0,0,1,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,1,0,1,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
[1,1,1,0,0,0]
=> []
=> []
=> [1] => ? = 0 + 2
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 0 + 2
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 1 + 2
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 2
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 0 + 2
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => ? = 1 + 2
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 0 + 2
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 0 + 2
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 0 + 2
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,1,1,0,1,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
[1,1,1,1,0,0,0,0]
=> []
=> []
=> [1] => ? = 0 + 2
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => ? = 0 + 2
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => ? = 0 + 2
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => ? = 0 + 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => ? = 1 + 2
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => ? = 0 + 2
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => ? = 0 + 2
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => ? = 0 + 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 0 + 2
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => ? = 0 + 2
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 0 + 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 0 + 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 0 + 2
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => ? = 0 + 2
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ? = 1 + 2
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => ? = 0 + 2
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => ? = 0 + 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => ? = 0 + 2
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => ? = 0 + 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => ? = 0 + 2
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => ? = 0 + 2
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 2 + 2
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 1 + 2
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => ? = 0 + 2
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 0 + 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => ? = 1 + 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => ? = 0 + 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => ? = 0 + 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => ? = 1 + 2
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 0 + 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => ? = 0 + 2
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 0 + 2
[1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => ? = 0 + 2
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 0 + 2
[1,1,1,1,0,0,1,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,0,1,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
=> [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
=> [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
=> [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> [1]
=> [1,0,1,0]
=> [3,1,2] => 2 = 0 + 2
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St000488
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000488: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00201: Dyck paths —Ringel⟶ Permutations
St000488: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [1,1,0,0]
=> [2,3,1] => 0
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 0
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 0
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => 0
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => 0
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => 0
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => 0
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => 0
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => 0
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => 0
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => 0
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => 0
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => 0
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => 0
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => 0
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [6,3,4,5,1,2] => 0
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [7,6,1,2,3,4,5] => ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [5,6,1,2,3,7,4] => ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [7,4,1,2,6,3,5] => ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [5,7,1,2,6,3,4] => ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [5,4,1,2,6,7,3] => ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [7,3,1,6,2,4,5] => ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [6,3,1,5,2,7,4] => ? = 0
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [7,4,1,6,2,3,5] => ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [6,7,1,5,2,3,4] => ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [6,4,1,5,2,7,3] => ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [4,3,1,7,6,2,5] => ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [7,3,1,5,6,2,4] => ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [7,4,1,5,6,2,3] => ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [4,3,1,5,6,7,2] => ? = 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [2,6,7,1,3,4,5] => ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [2,6,5,1,3,7,4] => ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [2,7,4,1,6,3,5] => ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [2,7,5,1,6,3,4] => ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,5,4,1,6,7,3] => ? = 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [6,3,7,1,2,4,5] => ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [6,3,5,1,2,7,4] => ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [6,7,4,1,2,3,5] => ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [6,7,5,1,2,3,4] => ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [6,5,4,1,2,7,3] => ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [7,3,4,1,6,2,5] => ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [7,3,5,1,6,2,4] => ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [7,5,4,1,6,2,3] => ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [5,3,4,1,6,7,2] => ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,3,7,6,1,4,5] => ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [2,3,6,5,1,7,4] => ? = 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,7,4,6,1,3,5] => ? = 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,7,6,5,1,3,4] => ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,6,4,5,1,7,3] => ? = 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [7,3,4,6,1,2,5] => ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [7,3,6,5,1,2,4] => ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [7,6,4,5,1,2,3] => ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [6,3,4,5,1,7,2] => ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [2,3,4,7,6,1,5] => ? = 0
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [2,3,7,5,6,1,4] => ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,7,4,5,6,1,3] => ? = 0
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [7,3,4,5,6,1,2] => ? = 0
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
[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]
=> [8,7,1,2,3,4,5,6] => ? = 0
[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]
=> [7,6,1,2,3,4,8,5] => ? = 0
[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]
=> [5,8,1,2,3,7,4,6] => ? = 0
[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]
=> [8,6,1,2,3,7,4,5] => ? = 0
[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]
=> [5,6,1,2,3,7,8,4] => ? = 0
[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]
=> [8,4,1,2,7,3,5,6] => ? = 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]
=> [7,4,1,2,6,3,8,5] => ? = 1
[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]
=> [5,8,1,2,7,3,4,6] => ? = 0
Description
The number of cycles of a permutation of length at most 2.
Matching statistic: St000214
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St000214: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St000214: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [(1,2)]
=> [2,1] => [1,2] => 0
[1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => [1,4,2,3] => 0
[1,1,0,0]
=> [(1,4),(2,3)]
=> [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => [1,4,2,3,6,5] => 1
[1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,6,5,4,3] => [1,6,2,3,4,5] => 0
[1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [4,3,2,1,6,5] => [1,6,2,3,4,5] => 0
[1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> [6,3,2,5,4,1] => [1,2,5,3,4,6] => 0
[1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> [6,5,4,3,2,1] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => [1,4,2,3,6,5,8,7] => ? = 0
[1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,8,7,6,5] => [1,4,2,3,8,5,6,7] => ? = 1
[1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,6,5,4,3,8,7] => [1,6,2,3,8,4,5,7] => ? = 0
[1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => 0
[1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,8,7,6,5,4,3] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [4,3,2,1,6,5,8,7] => [1,6,2,3,4,5,8,7] => ? = 1
[1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [4,3,2,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => 0
[1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> [8,3,2,5,4,7,6,1] => [1,2,5,3,4,7,6,8] => ? = 1
[1,1,0,1,1,0,0,0]
=> [(1,8),(2,3),(4,7),(5,6)]
=> [8,3,2,7,6,5,4,1] => [1,2,7,3,4,5,6,8] => ? = 0
[1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [6,5,4,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> [8,5,4,3,2,7,6,1] => [1,2,7,3,4,5,6,8] => ? = 0
[1,1,1,0,1,0,0,0]
=> [(1,8),(2,7),(3,4),(5,6)]
=> [8,7,4,3,6,5,2,1] => [1,2,3,6,4,5,7,8] => 0
[1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> [2,1,4,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9)]
=> [2,1,4,3,6,5,10,9,8,7] => [1,4,2,3,6,5,10,7,8,9] => ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10)]
=> [2,1,4,3,8,7,6,5,10,9] => [1,4,2,3,8,5,10,6,7,9] => ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,10),(6,7),(8,9)]
=> [2,1,4,3,10,7,6,9,8,5] => [1,4,2,3,10,5,6,9,7,8] => ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8)]
=> [2,1,4,3,10,9,8,7,6,5] => [1,4,2,3,10,5,6,7,8,9] => ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10)]
=> [2,1,6,5,4,3,8,7,10,9] => [1,6,2,3,8,4,5,7,10,9] => ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,10),(8,9)]
=> [2,1,6,5,4,3,10,9,8,7] => [1,6,2,3,10,4,5,7,8,9] => ? = 0
[1,0,1,1,0,1,0,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10)]
=> [2,1,8,5,4,7,6,3,10,9] => [1,8,2,3,10,4,7,5,6,9] => ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> [2,1,10,5,4,7,6,9,8,3] => [1,10,2,3,4,7,5,6,9,8] => ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8)]
=> [2,1,10,5,4,9,8,7,6,3] => [1,10,2,3,4,9,5,6,7,8] => ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10)]
=> [2,1,8,7,6,5,4,3,10,9] => [1,8,2,3,10,4,5,6,7,9] => ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9)]
=> [2,1,10,7,6,5,4,9,8,3] => [1,10,2,3,4,9,5,6,7,8] => ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8)]
=> [2,1,10,9,6,5,8,7,4,3] => [1,10,2,3,4,5,8,6,7,9] => ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,10,9,8,7,6,5,4,3] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8),(9,10)]
=> [4,3,2,1,6,5,8,7,10,9] => [1,6,2,3,4,5,8,7,10,9] => ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [(1,4),(2,3),(5,6),(7,10),(8,9)]
=> [4,3,2,1,6,5,10,9,8,7] => [1,6,2,3,4,5,10,7,8,9] => ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [(1,4),(2,3),(5,8),(6,7),(9,10)]
=> [4,3,2,1,8,7,6,5,10,9] => [1,8,2,3,4,5,10,6,7,9] => ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9)]
=> [4,3,2,1,10,7,6,9,8,5] => [1,10,2,3,4,5,6,9,7,8] => ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [4,3,2,1,10,9,8,7,6,5] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8),(9,10)]
=> [6,3,2,5,4,1,8,7,10,9] => [1,8,2,5,3,4,6,7,10,9] => ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [(1,6),(2,3),(4,5),(7,10),(8,9)]
=> [6,3,2,5,4,1,10,9,8,7] => [1,10,2,5,3,4,6,7,8,9] => ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [(1,8),(2,3),(4,5),(6,7),(9,10)]
=> [8,3,2,5,4,7,6,1,10,9] => [1,10,2,5,3,4,7,6,8,9] => ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> [10,3,2,5,4,7,6,9,8,1] => [1,2,5,3,4,7,6,9,8,10] => ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [(1,10),(2,3),(4,5),(6,9),(7,8)]
=> [10,3,2,5,4,9,8,7,6,1] => [1,2,5,3,4,9,6,7,8,10] => ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [(1,8),(2,3),(4,7),(5,6),(9,10)]
=> [8,3,2,7,6,5,4,1,10,9] => [1,10,2,7,3,4,5,6,8,9] => ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [(1,10),(2,3),(4,7),(5,6),(8,9)]
=> [10,3,2,7,6,5,4,9,8,1] => [1,2,7,3,4,9,5,6,8,10] => ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [(1,10),(2,3),(4,9),(5,6),(7,8)]
=> [10,3,2,9,6,5,8,7,4,1] => [1,2,9,3,4,5,8,6,7,10] => ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [(1,10),(2,3),(4,9),(5,8),(6,7)]
=> [10,3,2,9,8,7,6,5,4,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8),(9,10)]
=> [6,5,4,3,2,1,8,7,10,9] => [1,8,2,3,4,5,6,7,10,9] => ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [6,5,4,3,2,1,10,9,8,7] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [(1,8),(2,5),(3,4),(6,7),(9,10)]
=> [8,5,4,3,2,7,6,1,10,9] => [1,10,2,7,3,4,5,6,8,9] => ? = 0
[1,1,1,0,0,1,0,1,0,0]
=> [(1,10),(2,5),(3,4),(6,7),(8,9)]
=> [10,5,4,3,2,7,6,9,8,1] => [1,2,7,3,4,5,6,9,8,10] => ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [(1,10),(2,5),(3,4),(6,9),(7,8)]
=> [10,5,4,3,2,9,8,7,6,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,0,1,0,0,0,1,0]
=> [(1,8),(2,7),(3,4),(5,6),(9,10)]
=> [8,7,4,3,6,5,2,1,10,9] => [1,10,2,3,6,4,5,7,8,9] => ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [(1,10),(2,7),(3,4),(5,6),(8,9)]
=> [10,7,4,3,6,5,2,9,8,1] => [1,2,9,3,6,4,5,7,8,10] => ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [(1,10),(2,9),(3,4),(5,6),(7,8)]
=> [10,9,4,3,6,5,8,7,2,1] => [1,2,3,6,4,5,8,7,9,10] => ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [(1,10),(2,9),(3,4),(5,8),(6,7)]
=> [10,9,4,3,8,7,6,5,2,1] => [1,2,3,8,4,5,6,7,9,10] => ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [8,7,6,5,4,3,2,1,10,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,1,0,0]
=> [(1,10),(2,7),(3,6),(4,5),(8,9)]
=> [10,7,6,5,4,3,2,9,8,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [(1,10),(2,9),(3,6),(4,5),(7,8)]
=> [10,9,6,5,4,3,8,7,2,1] => [1,2,3,8,4,5,6,7,9,10] => ? = 0
[1,1,1,1,0,1,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,5),(6,7)]
=> [10,9,8,5,4,7,6,3,2,1] => [1,2,3,4,7,5,6,8,9,10] => ? = 0
[1,1,1,1,1,0,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,7),(5,6)]
=> [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]
=> [2,1,4,3,6,5,8,7,10,9,12,11] => [1,4,2,3,6,5,8,7,10,9,12,11] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]
=> [2,1,4,3,6,5,8,7,12,11,10,9] => [1,4,2,3,6,5,8,7,12,9,10,11] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]
=> [2,1,4,3,6,5,10,9,8,7,12,11] => [1,4,2,3,6,5,10,7,12,8,9,11] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]
=> [2,1,4,3,6,5,12,9,8,11,10,7] => [1,4,2,3,6,5,12,7,8,11,9,10] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]
=> [2,1,4,3,6,5,12,11,10,9,8,7] => [1,4,2,3,6,5,12,7,8,9,10,11] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]
=> [2,1,4,3,8,7,6,5,10,9,12,11] => [1,4,2,3,8,5,10,6,7,9,12,11] => ? = 2
Description
The number of adjacencies of a permutation.
An adjacency of a permutation $\pi$ is an index $i$ such that $\pi(i)-1 = \pi(i+1)$. Adjacencies are also known as ''small descents''.
This can be also described as an occurrence of the bivincular pattern ([2,1], {((0,1),(1,0),(1,1),(1,2),(2,1)}), i.e., the middle row and the middle column are shaded, see [3].
Matching statistic: St000215
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St000215: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St000215: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [(1,2)]
=> [2,1] => [1,2] => 0
[1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => [1,4,2,3] => 0
[1,1,0,0]
=> [(1,4),(2,3)]
=> [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => [1,4,2,3,6,5] => 1
[1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,6,5,4,3] => [1,6,2,3,4,5] => 0
[1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [4,3,2,1,6,5] => [1,6,2,3,4,5] => 0
[1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> [6,3,2,5,4,1] => [1,2,5,3,4,6] => 0
[1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> [6,5,4,3,2,1] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => [1,4,2,3,6,5,8,7] => ? = 0
[1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,8,7,6,5] => [1,4,2,3,8,5,6,7] => ? = 1
[1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,6,5,4,3,8,7] => [1,6,2,3,8,4,5,7] => ? = 0
[1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => 0
[1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,8,7,6,5,4,3] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [4,3,2,1,6,5,8,7] => [1,6,2,3,4,5,8,7] => ? = 1
[1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [4,3,2,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => 0
[1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> [8,3,2,5,4,7,6,1] => [1,2,5,3,4,7,6,8] => ? = 1
[1,1,0,1,1,0,0,0]
=> [(1,8),(2,3),(4,7),(5,6)]
=> [8,3,2,7,6,5,4,1] => [1,2,7,3,4,5,6,8] => ? = 0
[1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [6,5,4,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> [8,5,4,3,2,7,6,1] => [1,2,7,3,4,5,6,8] => ? = 0
[1,1,1,0,1,0,0,0]
=> [(1,8),(2,7),(3,4),(5,6)]
=> [8,7,4,3,6,5,2,1] => [1,2,3,6,4,5,7,8] => 0
[1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> [2,1,4,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9)]
=> [2,1,4,3,6,5,10,9,8,7] => [1,4,2,3,6,5,10,7,8,9] => ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10)]
=> [2,1,4,3,8,7,6,5,10,9] => [1,4,2,3,8,5,10,6,7,9] => ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,10),(6,7),(8,9)]
=> [2,1,4,3,10,7,6,9,8,5] => [1,4,2,3,10,5,6,9,7,8] => ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8)]
=> [2,1,4,3,10,9,8,7,6,5] => [1,4,2,3,10,5,6,7,8,9] => ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10)]
=> [2,1,6,5,4,3,8,7,10,9] => [1,6,2,3,8,4,5,7,10,9] => ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,10),(8,9)]
=> [2,1,6,5,4,3,10,9,8,7] => [1,6,2,3,10,4,5,7,8,9] => ? = 0
[1,0,1,1,0,1,0,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10)]
=> [2,1,8,5,4,7,6,3,10,9] => [1,8,2,3,10,4,7,5,6,9] => ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> [2,1,10,5,4,7,6,9,8,3] => [1,10,2,3,4,7,5,6,9,8] => ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8)]
=> [2,1,10,5,4,9,8,7,6,3] => [1,10,2,3,4,9,5,6,7,8] => ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10)]
=> [2,1,8,7,6,5,4,3,10,9] => [1,8,2,3,10,4,5,6,7,9] => ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9)]
=> [2,1,10,7,6,5,4,9,8,3] => [1,10,2,3,4,9,5,6,7,8] => ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8)]
=> [2,1,10,9,6,5,8,7,4,3] => [1,10,2,3,4,5,8,6,7,9] => ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,10,9,8,7,6,5,4,3] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8),(9,10)]
=> [4,3,2,1,6,5,8,7,10,9] => [1,6,2,3,4,5,8,7,10,9] => ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [(1,4),(2,3),(5,6),(7,10),(8,9)]
=> [4,3,2,1,6,5,10,9,8,7] => [1,6,2,3,4,5,10,7,8,9] => ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [(1,4),(2,3),(5,8),(6,7),(9,10)]
=> [4,3,2,1,8,7,6,5,10,9] => [1,8,2,3,4,5,10,6,7,9] => ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9)]
=> [4,3,2,1,10,7,6,9,8,5] => [1,10,2,3,4,5,6,9,7,8] => ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [4,3,2,1,10,9,8,7,6,5] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8),(9,10)]
=> [6,3,2,5,4,1,8,7,10,9] => [1,8,2,5,3,4,6,7,10,9] => ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [(1,6),(2,3),(4,5),(7,10),(8,9)]
=> [6,3,2,5,4,1,10,9,8,7] => [1,10,2,5,3,4,6,7,8,9] => ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [(1,8),(2,3),(4,5),(6,7),(9,10)]
=> [8,3,2,5,4,7,6,1,10,9] => [1,10,2,5,3,4,7,6,8,9] => ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> [10,3,2,5,4,7,6,9,8,1] => [1,2,5,3,4,7,6,9,8,10] => ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [(1,10),(2,3),(4,5),(6,9),(7,8)]
=> [10,3,2,5,4,9,8,7,6,1] => [1,2,5,3,4,9,6,7,8,10] => ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [(1,8),(2,3),(4,7),(5,6),(9,10)]
=> [8,3,2,7,6,5,4,1,10,9] => [1,10,2,7,3,4,5,6,8,9] => ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [(1,10),(2,3),(4,7),(5,6),(8,9)]
=> [10,3,2,7,6,5,4,9,8,1] => [1,2,7,3,4,9,5,6,8,10] => ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [(1,10),(2,3),(4,9),(5,6),(7,8)]
=> [10,3,2,9,6,5,8,7,4,1] => [1,2,9,3,4,5,8,6,7,10] => ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [(1,10),(2,3),(4,9),(5,8),(6,7)]
=> [10,3,2,9,8,7,6,5,4,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8),(9,10)]
=> [6,5,4,3,2,1,8,7,10,9] => [1,8,2,3,4,5,6,7,10,9] => ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [6,5,4,3,2,1,10,9,8,7] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [(1,8),(2,5),(3,4),(6,7),(9,10)]
=> [8,5,4,3,2,7,6,1,10,9] => [1,10,2,7,3,4,5,6,8,9] => ? = 0
[1,1,1,0,0,1,0,1,0,0]
=> [(1,10),(2,5),(3,4),(6,7),(8,9)]
=> [10,5,4,3,2,7,6,9,8,1] => [1,2,7,3,4,5,6,9,8,10] => ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [(1,10),(2,5),(3,4),(6,9),(7,8)]
=> [10,5,4,3,2,9,8,7,6,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,0,1,0,0,0,1,0]
=> [(1,8),(2,7),(3,4),(5,6),(9,10)]
=> [8,7,4,3,6,5,2,1,10,9] => [1,10,2,3,6,4,5,7,8,9] => ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [(1,10),(2,7),(3,4),(5,6),(8,9)]
=> [10,7,4,3,6,5,2,9,8,1] => [1,2,9,3,6,4,5,7,8,10] => ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [(1,10),(2,9),(3,4),(5,6),(7,8)]
=> [10,9,4,3,6,5,8,7,2,1] => [1,2,3,6,4,5,8,7,9,10] => ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [(1,10),(2,9),(3,4),(5,8),(6,7)]
=> [10,9,4,3,8,7,6,5,2,1] => [1,2,3,8,4,5,6,7,9,10] => ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [8,7,6,5,4,3,2,1,10,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,1,0,0]
=> [(1,10),(2,7),(3,6),(4,5),(8,9)]
=> [10,7,6,5,4,3,2,9,8,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [(1,10),(2,9),(3,6),(4,5),(7,8)]
=> [10,9,6,5,4,3,8,7,2,1] => [1,2,3,8,4,5,6,7,9,10] => ? = 0
[1,1,1,1,0,1,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,5),(6,7)]
=> [10,9,8,5,4,7,6,3,2,1] => [1,2,3,4,7,5,6,8,9,10] => ? = 0
[1,1,1,1,1,0,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,7),(5,6)]
=> [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]
=> [2,1,4,3,6,5,8,7,10,9,12,11] => [1,4,2,3,6,5,8,7,10,9,12,11] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]
=> [2,1,4,3,6,5,8,7,12,11,10,9] => [1,4,2,3,6,5,8,7,12,9,10,11] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]
=> [2,1,4,3,6,5,10,9,8,7,12,11] => [1,4,2,3,6,5,10,7,12,8,9,11] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]
=> [2,1,4,3,6,5,12,9,8,11,10,7] => [1,4,2,3,6,5,12,7,8,11,9,10] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]
=> [2,1,4,3,6,5,12,11,10,9,8,7] => [1,4,2,3,6,5,12,7,8,9,10,11] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]
=> [2,1,4,3,8,7,6,5,10,9,12,11] => [1,4,2,3,8,5,10,6,7,9,12,11] => ? = 2
Description
The number of adjacencies of a permutation, zero appended.
An adjacency is a descent of the form $(e+1,e)$ in the word corresponding to the permutation in one-line notation. This statistic, $\operatorname{adj_0}$, counts adjacencies in the word with a zero appended.
$(\operatorname{adj_0}, \operatorname{des})$ and $(\operatorname{fix}, \operatorname{exc})$ are equidistributed, see [1].
Matching statistic: St001465
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St001465: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St001465: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,0]
=> [(1,2)]
=> [2,1] => [1,2] => 0
[1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => [1,4,2,3] => 0
[1,1,0,0]
=> [(1,4),(2,3)]
=> [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => [1,4,2,3,6,5] => 1
[1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,6,5,4,3] => [1,6,2,3,4,5] => 0
[1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [4,3,2,1,6,5] => [1,6,2,3,4,5] => 0
[1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> [6,3,2,5,4,1] => [1,2,5,3,4,6] => 0
[1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> [6,5,4,3,2,1] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => [1,4,2,3,6,5,8,7] => ? = 0
[1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,8,7,6,5] => [1,4,2,3,8,5,6,7] => ? = 1
[1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,6,5,4,3,8,7] => [1,6,2,3,8,4,5,7] => ? = 0
[1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => 0
[1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,8,7,6,5,4,3] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [4,3,2,1,6,5,8,7] => [1,6,2,3,4,5,8,7] => ? = 1
[1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [4,3,2,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => 0
[1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> [8,3,2,5,4,7,6,1] => [1,2,5,3,4,7,6,8] => ? = 1
[1,1,0,1,1,0,0,0]
=> [(1,8),(2,3),(4,7),(5,6)]
=> [8,3,2,7,6,5,4,1] => [1,2,7,3,4,5,6,8] => ? = 0
[1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [6,5,4,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => 0
[1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> [8,5,4,3,2,7,6,1] => [1,2,7,3,4,5,6,8] => ? = 0
[1,1,1,0,1,0,0,0]
=> [(1,8),(2,7),(3,4),(5,6)]
=> [8,7,4,3,6,5,2,1] => [1,2,3,6,4,5,7,8] => 0
[1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> [2,1,4,3,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => ? = 0
[1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9)]
=> [2,1,4,3,6,5,10,9,8,7] => [1,4,2,3,6,5,10,7,8,9] => ? = 0
[1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10)]
=> [2,1,4,3,8,7,6,5,10,9] => [1,4,2,3,8,5,10,6,7,9] => ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,10),(6,7),(8,9)]
=> [2,1,4,3,10,7,6,9,8,5] => [1,4,2,3,10,5,6,9,7,8] => ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8)]
=> [2,1,4,3,10,9,8,7,6,5] => [1,4,2,3,10,5,6,7,8,9] => ? = 1
[1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10)]
=> [2,1,6,5,4,3,8,7,10,9] => [1,6,2,3,8,4,5,7,10,9] => ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,10),(8,9)]
=> [2,1,6,5,4,3,10,9,8,7] => [1,6,2,3,10,4,5,7,8,9] => ? = 0
[1,0,1,1,0,1,0,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10)]
=> [2,1,8,5,4,7,6,3,10,9] => [1,8,2,3,10,4,7,5,6,9] => ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> [2,1,10,5,4,7,6,9,8,3] => [1,10,2,3,4,7,5,6,9,8] => ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8)]
=> [2,1,10,5,4,9,8,7,6,3] => [1,10,2,3,4,9,5,6,7,8] => ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10)]
=> [2,1,8,7,6,5,4,3,10,9] => [1,8,2,3,10,4,5,6,7,9] => ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9)]
=> [2,1,10,7,6,5,4,9,8,3] => [1,10,2,3,4,9,5,6,7,8] => ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8)]
=> [2,1,10,9,6,5,8,7,4,3] => [1,10,2,3,4,5,8,6,7,9] => ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,10,9,8,7,6,5,4,3] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8),(9,10)]
=> [4,3,2,1,6,5,8,7,10,9] => [1,6,2,3,4,5,8,7,10,9] => ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [(1,4),(2,3),(5,6),(7,10),(8,9)]
=> [4,3,2,1,6,5,10,9,8,7] => [1,6,2,3,4,5,10,7,8,9] => ? = 1
[1,1,0,0,1,1,0,0,1,0]
=> [(1,4),(2,3),(5,8),(6,7),(9,10)]
=> [4,3,2,1,8,7,6,5,10,9] => [1,8,2,3,4,5,10,6,7,9] => ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9)]
=> [4,3,2,1,10,7,6,9,8,5] => [1,10,2,3,4,5,6,9,7,8] => ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [4,3,2,1,10,9,8,7,6,5] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8),(9,10)]
=> [6,3,2,5,4,1,8,7,10,9] => [1,8,2,5,3,4,6,7,10,9] => ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [(1,6),(2,3),(4,5),(7,10),(8,9)]
=> [6,3,2,5,4,1,10,9,8,7] => [1,10,2,5,3,4,6,7,8,9] => ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [(1,8),(2,3),(4,5),(6,7),(9,10)]
=> [8,3,2,5,4,7,6,1,10,9] => [1,10,2,5,3,4,7,6,8,9] => ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> [10,3,2,5,4,7,6,9,8,1] => [1,2,5,3,4,7,6,9,8,10] => ? = 2
[1,1,0,1,0,1,1,0,0,0]
=> [(1,10),(2,3),(4,5),(6,9),(7,8)]
=> [10,3,2,5,4,9,8,7,6,1] => [1,2,5,3,4,9,6,7,8,10] => ? = 1
[1,1,0,1,1,0,0,0,1,0]
=> [(1,8),(2,3),(4,7),(5,6),(9,10)]
=> [8,3,2,7,6,5,4,1,10,9] => [1,10,2,7,3,4,5,6,8,9] => ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [(1,10),(2,3),(4,7),(5,6),(8,9)]
=> [10,3,2,7,6,5,4,9,8,1] => [1,2,7,3,4,9,5,6,8,10] => ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [(1,10),(2,3),(4,9),(5,6),(7,8)]
=> [10,3,2,9,6,5,8,7,4,1] => [1,2,9,3,4,5,8,6,7,10] => ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [(1,10),(2,3),(4,9),(5,8),(6,7)]
=> [10,3,2,9,8,7,6,5,4,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8),(9,10)]
=> [6,5,4,3,2,1,8,7,10,9] => [1,8,2,3,4,5,6,7,10,9] => ? = 1
[1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [6,5,4,3,2,1,10,9,8,7] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,1,0,0,1,0]
=> [(1,8),(2,5),(3,4),(6,7),(9,10)]
=> [8,5,4,3,2,7,6,1,10,9] => [1,10,2,7,3,4,5,6,8,9] => ? = 0
[1,1,1,0,0,1,0,1,0,0]
=> [(1,10),(2,5),(3,4),(6,7),(8,9)]
=> [10,5,4,3,2,7,6,9,8,1] => [1,2,7,3,4,5,6,9,8,10] => ? = 1
[1,1,1,0,0,1,1,0,0,0]
=> [(1,10),(2,5),(3,4),(6,9),(7,8)]
=> [10,5,4,3,2,9,8,7,6,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,0,1,0,0,0,1,0]
=> [(1,8),(2,7),(3,4),(5,6),(9,10)]
=> [8,7,4,3,6,5,2,1,10,9] => [1,10,2,3,6,4,5,7,8,9] => ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [(1,10),(2,7),(3,4),(5,6),(8,9)]
=> [10,7,4,3,6,5,2,9,8,1] => [1,2,9,3,6,4,5,7,8,10] => ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [(1,10),(2,9),(3,4),(5,6),(7,8)]
=> [10,9,4,3,6,5,8,7,2,1] => [1,2,3,6,4,5,8,7,9,10] => ? = 1
[1,1,1,0,1,1,0,0,0,0]
=> [(1,10),(2,9),(3,4),(5,8),(6,7)]
=> [10,9,4,3,8,7,6,5,2,1] => [1,2,3,8,4,5,6,7,9,10] => ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [8,7,6,5,4,3,2,1,10,9] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,0,0,0,1,0,0]
=> [(1,10),(2,7),(3,6),(4,5),(8,9)]
=> [10,7,6,5,4,3,2,9,8,1] => [1,2,9,3,4,5,6,7,8,10] => ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [(1,10),(2,9),(3,6),(4,5),(7,8)]
=> [10,9,6,5,4,3,8,7,2,1] => [1,2,3,8,4,5,6,7,9,10] => ? = 0
[1,1,1,1,0,1,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,5),(6,7)]
=> [10,9,8,5,4,7,6,3,2,1] => [1,2,3,4,7,5,6,8,9,10] => ? = 0
[1,1,1,1,1,0,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,7),(5,6)]
=> [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]
=> [2,1,4,3,6,5,8,7,10,9,12,11] => [1,4,2,3,6,5,8,7,10,9,12,11] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]
=> [2,1,4,3,6,5,8,7,12,11,10,9] => [1,4,2,3,6,5,8,7,12,9,10,11] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]
=> [2,1,4,3,6,5,10,9,8,7,12,11] => [1,4,2,3,6,5,10,7,12,8,9,11] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]
=> [2,1,4,3,6,5,12,9,8,11,10,7] => [1,4,2,3,6,5,12,7,8,11,9,10] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]
=> [2,1,4,3,6,5,12,11,10,9,8,7] => [1,4,2,3,6,5,12,7,8,9,10,11] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]
=> [2,1,4,3,8,7,6,5,10,9,12,11] => [1,4,2,3,8,5,10,6,7,9,12,11] => ? = 2
Description
The number of adjacent transpositions in the cycle decomposition of a permutation.
The following 1 statistic also match your data. Click on any of them to see the details.
St000883The number of longest increasing subsequences of a permutation.
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