Identifier
Values
[1] => [[1]] => [1] => ([],1) => 0
[1,1] => [[1],[2]] => [1,1] => ([(0,1)],2) => 1
[1,1,1] => [[1],[2],[3]] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 1
[1,1,1,1] => [[1],[2],[3],[4]] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,1,1,1,1] => [[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
[1,1,1,1,1,1] => [[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
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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) => 1
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.