Identifier
Values
[[1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1],[2]] => ([],1) => ([],1) => 0
[[1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2]] => ([],1) => ([],1) => 0
[[1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2,2]] => ([],1) => ([],1) => 0
[[1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1],[2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,2,2]] => ([],1) => ([],1) => 0
[[1],[2],[3],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1],[2,2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2],[3],[4]] => ([],1) => ([],1) => 0
[[1,2],[2],[3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,2,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[1,1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,2],[2,2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2,2],[3,3]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2,2]] => ([],1) => ([],1) => 0
[[1,1,1,2],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2],[3],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,2],[2],[3],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1],[2],[3],[4],[5]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,2],[2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1],[2,2],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,2],[2,2],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1],[2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1,2],[2],[3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2,2],[3,4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1],[2,2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1],[2,3],[3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,1,2],[2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,2],[2,2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,2,2],[3]] => ([],1) => ([],1) => 0
[[1,1,1],[2,2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1],[2,2],[3,3]] => ([],1) => ([],1) => 0
[[1,1,2],[2,2],[3,3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1,1,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,2],[2,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2,2,2]] => ([],1) => ([],1) => 0
[[1,1,1,1,2],[2,2,2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2,2,2]] => ([],1) => ([],1) => 0
[[1]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2,2,2],[3,3],[4]] => ([],1) => ([],1) => 0
[[1,1,1,2],[2,2,2],[3,3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2,3],[3,3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1],[2,2,2],[3,4],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,2],[2,2,2],[3,4],[4]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => ([],1) => ([],1) => 0
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
>>> Load all 123 entries. <<<
[[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,1]] => ([],1) => ([],1) => 0
[[1,1,1]] => ([],1) => ([],1) => 0
[[1,1,1,1]] => ([],1) => ([],1) => 0
[[1,1,1,1,1]] => ([],1) => ([],1) => 0
[[1],[2],[3],[4],[5],[6]] => ([],1) => ([],1) => 0
search for individual values
searching the database for the individual values of this statistic
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.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
subcrystal
Description
The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.