Identifier
Values
[[1]] => [[1]] => ([],1) => ([],1) => 0
[[1,0],[0,1]] => [[1,1],[2]] => ([],1) => ([],1) => 0
[[0,1],[1,0]] => [[1,2],[2]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0],[0,1,0],[0,0,1]] => [[1,1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[0,1,0],[1,0,0],[0,0,1]] => [[1,1,2],[2,2],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0],[0,0,1],[0,1,0]] => [[1,1,1],[2,3],[3]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => [[1,1,1,1],[2,2,2],[3,3],[4]] => ([],1) => ([],1) => 0
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]] => [[1,1,1,2],[2,2,2],[3,3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]] => [[1,1,1,1],[2,2,3],[3,3],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => [[1,1,1,1],[2,2,2],[3,4],[4]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] => [[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
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => ([],1) => ([],1) => 0
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => [[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
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => ([(0,1)],2) => ([(0,1)],2) => 1
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[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
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [[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
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => ([],1) => ([],1) => 0
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[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
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[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
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[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
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [[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
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[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
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[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
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [[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
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[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
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[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
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[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
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [[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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
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
to semistandard tableau via monotone triangles
Description
The semistandard tableau corresponding the monotone triangle of an alternating sign matrix.
This is obtained by interpreting each row of the monotone triangle as an integer partition, and filling the cells of the smallest partition with ones, the second smallest with twos, and so on.
Map
subcrystal
Description
The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.