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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000729
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St000729: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 1
{{1},{2}}
=> 2
{{1,2,3}}
=> 1
{{1,2},{3}}
=> 1
{{1,3},{2}}
=> 2
{{1},{2,3}}
=> 1
{{1},{2},{3}}
=> 3
{{1,2,3,4}}
=> 1
{{1,2,3},{4}}
=> 1
{{1,2,4},{3}}
=> 1
{{1,2},{3,4}}
=> 1
{{1,2},{3},{4}}
=> 1
{{1,3,4},{2}}
=> 1
{{1,3},{2,4}}
=> 2
{{1,3},{2},{4}}
=> 2
{{1,4},{2,3}}
=> 1
{{1},{2,3,4}}
=> 1
{{1},{2,3},{4}}
=> 1
{{1,4},{2},{3}}
=> 3
{{1},{2,4},{3}}
=> 2
{{1},{2},{3,4}}
=> 1
{{1},{2},{3},{4}}
=> 4
{{1,2,3,4,5}}
=> 1
{{1,2,3,4},{5}}
=> 1
{{1,2,3,5},{4}}
=> 1
{{1,2,3},{4,5}}
=> 1
{{1,2,3},{4},{5}}
=> 1
{{1,2,4,5},{3}}
=> 1
{{1,2,4},{3,5}}
=> 1
{{1,2,4},{3},{5}}
=> 1
{{1,2,5},{3,4}}
=> 1
{{1,2},{3,4,5}}
=> 1
{{1,2},{3,4},{5}}
=> 1
{{1,2,5},{3},{4}}
=> 1
{{1,2},{3,5},{4}}
=> 1
{{1,2},{3},{4,5}}
=> 1
{{1,2},{3},{4},{5}}
=> 1
{{1,3,4,5},{2}}
=> 1
{{1,3,4},{2,5}}
=> 1
{{1,3,4},{2},{5}}
=> 1
{{1,3,5},{2,4}}
=> 2
{{1,3},{2,4,5}}
=> 1
{{1,3},{2,4},{5}}
=> 2
{{1,3,5},{2},{4}}
=> 2
{{1,3},{2,5},{4}}
=> 2
{{1,3},{2},{4,5}}
=> 1
{{1,3},{2},{4},{5}}
=> 2
{{1,4,5},{2,3}}
=> 1
{{1,4},{2,3,5}}
=> 1
{{1,4},{2,3},{5}}
=> 1
Description
The minimal arc length of a set partition.
The arcs of a set partition are those $i < j$ that are consecutive elements in the blocks. If there are no arcs, the minimal arc length is the size of the ground set (as the minimum of the empty set in the universe of arcs of length less than the size of the ground set).
Matching statistic: St000363
Mp00171: Set partitions —intertwining number to dual major index⟶ Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000363: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 96%●distinct values known / distinct values provided: 50%
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000363: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 96%●distinct values known / distinct values provided: 50%
Values
{{1,2}}
=> {{1,2}}
=> [2] => ([],2)
=> 1
{{1},{2}}
=> {{1},{2}}
=> [1,1] => ([(0,1)],2)
=> 2
{{1,2,3}}
=> {{1,2,3}}
=> [3] => ([],3)
=> 1
{{1,2},{3}}
=> {{1,2},{3}}
=> [2,1] => ([(0,2),(1,2)],3)
=> 1
{{1,3},{2}}
=> {{1},{2,3}}
=> [1,2] => ([(1,2)],3)
=> 2
{{1},{2,3}}
=> {{1,3},{2}}
=> [2,1] => ([(0,2),(1,2)],3)
=> 1
{{1},{2},{3}}
=> {{1},{2},{3}}
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
{{1,2,3,4}}
=> {{1,2,3,4}}
=> [4] => ([],4)
=> 1
{{1,2,3},{4}}
=> {{1,2,3},{4}}
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1,2,4},{3}}
=> {{1,2},{3,4}}
=> [2,2] => ([(1,3),(2,3)],4)
=> 1
{{1,2},{3,4}}
=> {{1,2,4},{3}}
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1,2},{3},{4}}
=> {{1,2},{3},{4}}
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1,3,4},{2}}
=> {{1,4},{2,3}}
=> [2,2] => ([(1,3),(2,3)],4)
=> 1
{{1,3},{2,4}}
=> {{1},{2,3,4}}
=> [1,3] => ([(2,3)],4)
=> 2
{{1,3},{2},{4}}
=> {{1},{2,3},{4}}
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
{{1,4},{2,3}}
=> {{1,3},{2,4}}
=> [2,2] => ([(1,3),(2,3)],4)
=> 1
{{1},{2,3,4}}
=> {{1,3,4},{2}}
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1},{2,3},{4}}
=> {{1,3},{2},{4}}
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1,4},{2},{3}}
=> {{1},{2},{3,4}}
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
{{1},{2,4},{3}}
=> {{1},{2,4},{3}}
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
{{1},{2},{3,4}}
=> {{1,4},{2},{3}}
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1},{2},{3},{4}}
=> {{1},{2},{3},{4}}
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
{{1,2,3,4,5}}
=> {{1,2,3,4,5}}
=> [5] => ([],5)
=> 1
{{1,2,3,4},{5}}
=> {{1,2,3,4},{5}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1,2,3,5},{4}}
=> {{1,2,3},{4,5}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 1
{{1,2,3},{4,5}}
=> {{1,2,3,5},{4}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1,2,3},{4},{5}}
=> {{1,2,3},{4},{5}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,4,5},{3}}
=> {{1,2,5},{3,4}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 1
{{1,2,4},{3,5}}
=> {{1,2},{3,4,5}}
=> [2,3] => ([(2,4),(3,4)],5)
=> 1
{{1,2,4},{3},{5}}
=> {{1,2},{3,4},{5}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,5},{3,4}}
=> {{1,2,4},{3,5}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 1
{{1,2},{3,4,5}}
=> {{1,2,4,5},{3}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1,2},{3,4},{5}}
=> {{1,2,4},{3},{5}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,5},{3},{4}}
=> {{1,2},{3},{4,5}}
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3,5},{4}}
=> {{1,2},{3,5},{4}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3},{4,5}}
=> {{1,2,5},{3},{4}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3},{4},{5}}
=> {{1,2},{3},{4},{5}}
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,3,4,5},{2}}
=> {{1,4,5},{2,3}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 1
{{1,3,4},{2,5}}
=> {{1,4},{2,3,5}}
=> [2,3] => ([(2,4),(3,4)],5)
=> 1
{{1,3,4},{2},{5}}
=> {{1,4},{2,3},{5}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,3,5},{2,4}}
=> {{1},{2,3,4,5}}
=> [1,4] => ([(3,4)],5)
=> 2
{{1,3},{2,4,5}}
=> {{1,5},{2,3,4}}
=> [2,3] => ([(2,4),(3,4)],5)
=> 1
{{1,3},{2,4},{5}}
=> {{1},{2,3,4},{5}}
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,3,5},{2},{4}}
=> {{1},{2,3,5},{4}}
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,3},{2,5},{4}}
=> {{1},{2,3},{4,5}}
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,3},{2},{4,5}}
=> {{1,5},{2,3},{4}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,3},{2},{4},{5}}
=> {{1},{2,3},{4},{5}}
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
{{1,4,5},{2,3}}
=> {{1,3,5},{2,4}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> 1
{{1,4},{2,3,5}}
=> {{1,3},{2,4,5}}
=> [2,3] => ([(2,4),(3,4)],5)
=> 1
{{1,4},{2,3},{5}}
=> {{1,3},{2,4},{5}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,4},{2,5},{3},{6},{7}}
=> {{1},{2},{3,4,5},{6},{7}}
=> [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
{{1,4},{2},{3,6},{5},{7}}
=> {{1},{2},{3,4,6},{5},{7}}
=> [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
{{1,4,7},{2},{3},{5},{6}}
=> {{1},{2},{3,4,7},{5},{6}}
=> [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
{{1},{2,5},{3,6},{4},{7}}
=> {{1},{2},{3,5,6},{4},{7}}
=> [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
{{1},{2,5},{3},{4,7},{6}}
=> {{1},{2},{3,5,7},{4},{6}}
=> [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
{{1},{2},{3,6},{4,7},{5}}
=> {{1},{2},{3,6,7},{4},{5}}
=> [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
{{1},{2},{3,4,5,6,7,8}}
=> {{1,4,5,6,7,8},{2},{3}}
=> [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,4,5,6,7,8},{3}}
=> {{1,5,6,7,8},{2,4},{3}}
=> [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,3,5,6,7,8},{4}}
=> {{1,3,6,7,8},{2,5},{4}}
=> [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,3,4,6,7,8},{5}}
=> {{1,3,4,7,8},{2,6},{5}}
=> [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,3,4,5,7,8},{6}}
=> {{1,3,4,5,8},{2,7},{6}}
=> [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,3,4,5,6,7},{8}}
=> {{1,3,4,5,6,7},{2},{8}}
=> [6,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,3,4,5,6,8},{7}}
=> {{1,3,4,5,6},{2,8},{7}}
=> [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1},{2,3,4,5,6,7,8}}
=> {{1,3,4,5,6,7,8},{2}}
=> [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2},{3,4,5,6,7,8}}
=> {{1,2,4,5,6,7,8},{3}}
=> [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,4,5,6,7,8},{2},{3}}
=> {{1,5,6,7,8},{2},{3,4}}
=> ? => ?
=> ? = 1
{{1,3,5,6,7,8},{2},{4}}
=> {{1,6,7,8},{2,3,5},{4}}
=> [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> ? = 1
{{1,3,4,5,6,7,8},{2}}
=> {{1,4,5,6,7,8},{2,3}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,4,5,6,7,8},{2,3}}
=> {{1,3,5,6,7,8},{2,4}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,4,5,6,7,8},{3}}
=> {{1,2,5,6,7,8},{3,4}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,5,6,7,8},{3,4}}
=> {{1,2,4,6,7,8},{3,5}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,5,6,7,8},{4}}
=> {{1,2,3,6,7,8},{4,5}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,6,7,8},{4,5}}
=> {{1,2,3,5,7,8},{4,6}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,6,7,8},{5}}
=> {{1,2,3,4,7,8},{5,6}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,5,6},{7,8}}
=> {{1,2,3,4,5,6,8},{7}}
=> [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = -1
{{1,2,3,4,7,8},{5,6}}
=> {{1,2,3,4,6,8},{5,7}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,5,7,8},{6}}
=> {{1,2,3,4,5,8},{6,7}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,5,6,7},{8}}
=> {{1,2,3,4,5,6,7},{8}}
=> [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,8},{2,3,4,5,6,7}}
=> {{1,3,4,5,6,7},{2,8}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = -7
{{1,2,3,4,5,8},{6,7}}
=> {{1,2,3,4,5,7},{6,8}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,5,6,8},{7}}
=> {{1,2,3,4,5,6},{7,8}}
=> [6,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,5,6,7,8}}
=> {{1,2,3,4,5,6,7,8}}
=> [8] => ([],8)
=> ? = 1
{{1,3,5,6,7,8},{2,4}}
=> {{1,6,7,8},{2,3,4,5}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,3,4,6,7,8},{2,5}}
=> {{1,4,7,8},{2,3,5,6}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,4,6,7,8},{3,5}}
=> {{1,2,7,8},{3,4,5,6}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,3,4,5,7,8},{2,6}}
=> {{1,4,5,8},{2,3,6,7}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,4,5,7,8},{3,6}}
=> {{1,2,5,8},{3,4,6,7}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,5,7,8},{4,6}}
=> {{1,2,3,8},{4,5,6,7}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,3,4,5,6,8},{2,7}}
=> {{1,4,5,6},{2,3,7,8}}
=> ? => ?
=> ? = 1
{{1,2,4,5,6,8},{3,7}}
=> {{1,2,5,6},{3,4,7,8}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,5,6,8},{4,7}}
=> {{1,2,3,6},{4,5,7,8}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,2,3,4,6,8},{5,7}}
=> {{1,2,3,4},{5,6,7,8}}
=> [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,3,4,5,6,7},{2,8}}
=> {{1,4,5,6,7},{2,3,8}}
=> ? => ?
=> ? = -6
{{1,2,4,5,6,7},{3,8}}
=> {{1,2,5,6,7},{3,4,8}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = -5
{{1,2,3,5,6,7},{4,8}}
=> {{1,2,3,6,7},{4,5,8}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = -4
{{1,2,3,4,6,7},{5,8}}
=> {{1,2,3,4,7},{5,6,8}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = -3
{{1,2,3,4,5,7},{6,8}}
=> {{1,2,3,4,5},{6,7,8}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = -2
{{1,3},{2,4,5,6,7,8}}
=> {{1,5,6,7,8},{2,3,4}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,4},{2,3,5,6,7,8}}
=> {{1,3,6,7,8},{2,4,5}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
{{1,5},{2,3,4,6,7,8}}
=> {{1,3,4,7,8},{2,5,6}}
=> [5,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
Description
The number of minimal vertex covers of a graph.
A '''vertex cover''' of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. A vertex cover is minimal if it contains the least possible number of vertices.
This is also the leading coefficient of the clique polynomial of the complement of $G$.
This is also the number of independent sets of maximal cardinality of $G$.
Matching statistic: St000260
Mp00221: Set partitions —conjugate⟶ Set partitions
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 57%●distinct values known / distinct values provided: 7%
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 57%●distinct values known / distinct values provided: 7%
Values
{{1,2}}
=> {{1},{2}}
=> [1,1] => ([(0,1)],2)
=> 1
{{1},{2}}
=> {{1,2}}
=> [2] => ([],2)
=> ? = 2
{{1,2,3}}
=> {{1},{2},{3}}
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
{{1,2},{3}}
=> {{1,2},{3}}
=> [2,1] => ([(0,2),(1,2)],3)
=> 1
{{1,3},{2}}
=> {{1},{2,3}}
=> [1,2] => ([(1,2)],3)
=> ? = 2
{{1},{2,3}}
=> {{1,3},{2}}
=> [2,1] => ([(0,2),(1,2)],3)
=> 1
{{1},{2},{3}}
=> {{1,2,3}}
=> [3] => ([],3)
=> ? = 3
{{1,2,3,4}}
=> {{1},{2},{3},{4}}
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1,2,3},{4}}
=> {{1,2},{3},{4}}
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1,2,4},{3}}
=> {{1},{2,3},{4}}
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1,2},{3,4}}
=> {{1,3},{2},{4}}
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1,2},{3},{4}}
=> {{1,2,3},{4}}
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1,3,4},{2}}
=> {{1},{2},{3,4}}
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 1
{{1,3},{2,4}}
=> {{1,3},{2,4}}
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
{{1,3},{2},{4}}
=> {{1,2},{3,4}}
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
{{1,4},{2,3}}
=> {{1},{2,4},{3}}
=> [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1},{2,3,4}}
=> {{1,4},{2},{3}}
=> [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
{{1},{2,3},{4}}
=> {{1,2,4},{3}}
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1,4},{2},{3}}
=> {{1},{2,3,4}}
=> [1,3] => ([(2,3)],4)
=> ? = 3
{{1},{2,4},{3}}
=> {{1,4},{2,3}}
=> [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
{{1},{2},{3,4}}
=> {{1,3,4},{2}}
=> [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
{{1},{2},{3},{4}}
=> {{1,2,3,4}}
=> [4] => ([],4)
=> ? = 4
{{1,2,3,4,5}}
=> {{1},{2},{3},{4},{5}}
=> [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,3,4},{5}}
=> {{1,2},{3},{4},{5}}
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,3,5},{4}}
=> {{1},{2,3},{4},{5}}
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,3},{4,5}}
=> {{1,3},{2},{4},{5}}
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,3},{4},{5}}
=> {{1,2,3},{4},{5}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,4,5},{3}}
=> {{1},{2},{3,4},{5}}
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,4},{3,5}}
=> {{1,3},{2,4},{5}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,4},{3},{5}}
=> {{1,2},{3,4},{5}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,5},{3,4}}
=> {{1},{2,4},{3},{5}}
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3,4,5}}
=> {{1,4},{2},{3},{5}}
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3,4},{5}}
=> {{1,2,4},{3},{5}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2,5},{3},{4}}
=> {{1},{2,3,4},{5}}
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3,5},{4}}
=> {{1,4},{2,3},{5}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3},{4,5}}
=> {{1,3,4},{2},{5}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,2},{3},{4},{5}}
=> {{1,2,3,4},{5}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1,3,4,5},{2}}
=> {{1},{2},{3},{4,5}}
=> [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
{{1,3,4},{2,5}}
=> {{1,4},{2,5},{3}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,3,4},{2},{5}}
=> {{1,2},{3},{4,5}}
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
{{1,3,5},{2,4}}
=> {{1},{2,4},{3,5}}
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2
{{1,3},{2,4,5}}
=> {{1,4},{2},{3,5}}
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
{{1,3},{2,4},{5}}
=> {{1,2,4},{3,5}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2
{{1,3,5},{2},{4}}
=> {{1},{2,3},{4,5}}
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2
{{1,3},{2,5},{4}}
=> {{1,4},{2,3,5}}
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 2
{{1,3},{2},{4,5}}
=> {{1,3},{2},{4,5}}
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
{{1,3},{2},{4},{5}}
=> {{1,2,3},{4,5}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2
{{1,4,5},{2,3}}
=> {{1},{2},{3,5},{4}}
=> [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,4},{2,3,5}}
=> {{1,3},{2,5},{4}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,4},{2,3},{5}}
=> {{1,2},{3,5},{4}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,5},{2,3,4}}
=> {{1},{2,5},{3},{4}}
=> [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2,3,4,5}}
=> {{1,5},{2},{3},{4}}
=> [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2,3,4},{5}}
=> {{1,2,5},{3},{4}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1,5},{2,3},{4}}
=> {{1},{2,3,5},{4}}
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2,3,5},{4}}
=> {{1,5},{2,3},{4}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2,3},{4,5}}
=> {{1,3,5},{2},{4}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2,3},{4},{5}}
=> {{1,2,3,5},{4}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1,4,5},{2},{3}}
=> {{1},{2},{3,4,5}}
=> [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 1
{{1,4},{2,5},{3}}
=> {{1,3,4},{2,5}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3
{{1,4},{2},{3,5}}
=> {{1,3},{2,4,5}}
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 2
{{1,4},{2},{3},{5}}
=> {{1,2},{3,4,5}}
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3
{{1,5},{2,4},{3}}
=> {{1},{2,5},{3,4}}
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 2
{{1},{2,4,5},{3}}
=> {{1,5},{2},{3,4}}
=> [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
{{1},{2,4},{3,5}}
=> {{1,3,5},{2,4}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2
{{1},{2,4},{3},{5}}
=> {{1,2,5},{3,4}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2
{{1,5},{2},{3,4}}
=> {{1},{2,4,5},{3}}
=> [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2,5},{3,4}}
=> {{1,5},{2,4},{3}}
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2},{3,4,5}}
=> {{1,4,5},{2},{3}}
=> [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
{{1},{2},{3,4},{5}}
=> {{1,2,4,5},{3}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1,5},{2},{3},{4}}
=> {{1},{2,3,4,5}}
=> [1,4] => ([(3,4)],5)
=> ? = 4
{{1},{2,5},{3},{4}}
=> {{1,5},{2,3,4}}
=> [2,3] => ([(2,4),(3,4)],5)
=> ? = 3
{{1},{2},{3,5},{4}}
=> {{1,4,5},{2,3}}
=> [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2
{{1},{2},{3},{4,5}}
=> {{1,3,4,5},{2}}
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
{{1},{2},{3},{4},{5}}
=> {{1,2,3,4,5}}
=> [5] => ([],5)
=> ? = 5
{{1,2,3,4,5,6}}
=> {{1},{2},{3},{4},{5},{6}}
=> [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
{{1,2,3,4,5},{6}}
=> {{1,2},{3},{4},{5},{6}}
=> [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
{{1,2,3,4,6},{5}}
=> {{1},{2,3},{4},{5},{6}}
=> [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
{{1,2,3,4},{5,6}}
=> {{1,3},{2},{4},{5},{6}}
=> [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
{{1,2,3,4},{5},{6}}
=> {{1,2,3},{4},{5},{6}}
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
{{1,2,3,5,6},{4}}
=> {{1},{2},{3,4},{5},{6}}
=> [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
{{1,3,4,5,6},{2}}
=> {{1},{2},{3},{4},{5,6}}
=> [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,4,5},{2},{6}}
=> {{1,2},{3},{4},{5,6}}
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,4,6},{2},{5}}
=> {{1},{2,3},{4},{5,6}}
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,4},{2},{5,6}}
=> {{1,3},{2},{4},{5,6}}
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,4},{2},{5},{6}}
=> {{1,2,3},{4},{5,6}}
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,5,6},{2,4}}
=> {{1},{2},{3,5},{4,6}}
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,5},{2,4,6}}
=> {{1,3,5},{2,4,6}}
=> [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 2
{{1,3,5},{2,4},{6}}
=> {{1,2},{3,5},{4,6}}
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
{{1,3,6},{2,4,5}}
=> {{1},{2,5},{3},{4,6}}
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3},{2,4,5,6}}
=> {{1,5},{2},{3},{4,6}}
=> [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3},{2,4,5},{6}}
=> {{1,2,5},{3},{4,6}}
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,6},{2,4},{5}}
=> {{1},{2,3,5},{4,6}}
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
{{1,3},{2,4,6},{5}}
=> {{1,5},{2,3},{4,6}}
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
{{1,3},{2,4},{5,6}}
=> {{1,3,5},{2},{4,6}}
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3},{2,4},{5},{6}}
=> {{1,2,3,5},{4,6}}
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2
{{1,3,5,6},{2},{4}}
=> {{1},{2},{3,4},{5,6}}
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
{{1,3,5},{2,6},{4}}
=> {{1,5},{2,6},{3,4}}
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
{{1,3,5},{2},{4,6}}
=> {{1,3},{2,4},{5,6}}
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
{{1,3,5},{2},{4},{6}}
=> {{1,2},{3,4},{5,6}}
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
{{1,3,6},{2,5},{4}}
=> {{1},{2,5},{3,4,6}}
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
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