Identifier
Values
[[1],[]] => ([],1) => ([],1) => 0
[[2],[]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[2,1],[1]] => ([],2) => ([],2) => 0
[[3,1],[1]] => ([(1,2)],3) => ([(1,2)],3) => 1
[[3,2],[2]] => ([(1,2)],3) => ([(1,2)],3) => 1
[[2,2,1],[1,1]] => ([(1,2)],3) => ([(1,2)],3) => 1
[[2,1,1],[1]] => ([(1,2)],3) => ([(1,2)],3) => 1
[[3,2,1],[2,1]] => ([],3) => ([],3) => 0
[[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[4,2],[2]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 1
[[3,1,1],[1]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 1
[[4,2,1],[2,1]] => ([(2,3)],4) => ([(2,3)],4) => 1
[[4,3,1],[3,1]] => ([(2,3)],4) => ([(2,3)],4) => 1
[[3,3,2],[2,2]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 1
[[4,3,2],[3,2]] => ([(2,3)],4) => ([(2,3)],4) => 1
[[2,2,1,1],[1,1]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => 1
[[3,3,2,1],[2,2,1]] => ([(2,3)],4) => ([(2,3)],4) => 1
[[3,2,2,1],[2,1,1]] => ([(2,3)],4) => ([(2,3)],4) => 1
[[3,2,1,1],[2,1]] => ([(2,3)],4) => ([(2,3)],4) => 1
[[4,3,2,1],[3,2,1]] => ([],4) => ([],4) => 0
[[3,3,1],[1,1]] => ([(1,2),(1,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 2
[[5,3,1],[3,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[5,3,2],[3,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[4,2,2,1],[2,1,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[4,2,1,1],[2,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[5,3,2,1],[3,2,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[3,2,2],[2]] => ([(1,2),(1,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => 2
[[5,4,2],[4,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[4,3,1,1],[3,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[5,4,2,1],[4,2,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[4,4,3,1],[3,3,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[5,4,3,1],[4,3,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[4,4,3,2],[3,3,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[4,3,3,2],[3,2,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[5,4,3,2],[4,3,2]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[3,3,2,2,1],[2,2,1,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[3,3,2,1,1],[2,2,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[4,4,3,2,1],[3,3,2,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[3,2,2,1,1],[2,1,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => 1
[[4,3,3,2,1],[3,2,2,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[4,3,2,2,1],[3,2,1,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[4,3,2,1,1],[3,2,1]] => ([(3,4)],5) => ([(3,4)],5) => 1
[[5,4,3,2,1],[4,3,2,1]] => ([],5) => ([],5) => 0
[[4,4,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 2
[[4,2,2],[2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 2
[[6,4,2],[4,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[3,3,1,1],[1,1]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 2
[[4,4,2,1],[2,2,1]] => ([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[[5,3,1,1],[3,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[6,4,2,1],[4,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,4,3,1],[4,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,3,3,2],[3,2,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[6,4,3,2],[4,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[4,2,2,1,1],[2,1,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[5,3,3,2,1],[3,2,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,3,2,2,1],[3,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,3,2,1,1],[3,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,4,3,2,1],[4,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[4,3,3,1],[3,1,1]] => ([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[[6,5,3,1],[5,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,5,3,2],[5,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,2,2,1],[4,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,2,1,1],[4,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,5,3,2,1],[5,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[3,3,2,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 2
[[5,5,4,2],[4,4,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[4,3,2,2],[3,2]] => ([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => 2
[[6,5,4,2],[5,4,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[4,4,3,1,1],[3,3,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[5,5,4,2,1],[4,4,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,3,1,1],[4,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,5,4,2,1],[5,4,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[5,5,4,3,1],[4,4,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,4,3,1],[4,3,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,5,4,3,1],[5,4,3,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[4,4,3,3,2],[3,3,2,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[5,5,4,3,2],[4,4,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,4,3,2],[4,3,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,3,3,2],[4,3,2,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[6,5,4,3,2],[5,4,3,2]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[3,3,2,2,1,1],[2,2,1,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => 1
[[4,4,3,3,2,1],[3,3,2,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[4,4,3,2,2,1],[3,3,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[4,4,3,2,1,1],[3,3,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,5,4,3,2,1],[4,4,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[4,3,3,2,2,1],[3,2,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[4,3,3,2,1,1],[3,2,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,4,3,2,1],[4,3,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[4,3,2,2,1,1],[3,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => 1
[[5,4,3,3,2,1],[4,3,2,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[5,4,3,2,2,1],[4,3,2,1,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[5,4,3,2,1,1],[4,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => 1
[[6,5,4,3,2,1],[5,4,3,2,1]] => ([],6) => ([],6) => 0
[[5,2,2],[2]] => ([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 2
[[5,5,3],[3,3]] => ([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 2
[[4,4,2,1],[2,2]] => ([(0,2),(0,3),(1,4),(1,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 2
[[5,5,3,1],[3,3,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 2
[[5,3,3,1],[3,1,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 2
[[7,5,3,1],[5,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => 1
[[4,4,2,2],[2,2,1]] => ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 2
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Description
The largest eigenvalue of a graph if it is integral.
If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell d is greater than a cell c if the entry in d must be larger than the entry of c in any standard Young tableau on the skew partition.
This is the poset on the cells of the Young diagram, such that a cell d is greater than a cell c if the entry in d must be larger than the entry of c in any standard Young tableau on the skew partition.
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