Identifier
Values
[[1],[2]] => ([],1) => ([],1) => 0
[[1,1],[2]] => ([],1) => ([],1) => 0
[[1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1],[2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,1],[2,2,2]] => ([],1) => ([],1) => 0
[[1,1],[2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[1,1],[2,2],[3,3]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2,2,2]] => ([],1) => ([],1) => 0
[[1],[2],[3],[4],[5]] => ([],1) => ([],1) => 0
[[1,1,1],[2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1],[2,2],[3],[4]] => ([],1) => ([],1) => 0
[[1,1,1,1,1],[2],[3]] => ([],1) => ([],1) => 0
[[1,1,1,1],[2,2],[3]] => ([],1) => ([],1) => 0
[[1,1,1],[2,2,2],[3]] => ([],1) => ([],1) => 0
[[1,1,1],[2,2],[3,3]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,1,1],[2]] => ([],1) => ([],1) => 0
[[1,1,1,1,1,1],[2,2]] => ([],1) => ([],1) => 0
[[1,1,1,1,1],[2,2,2]] => ([],1) => ([],1) => 0
[[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
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => ([],1) => ([],1) => 0
[[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) => 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 Gutman (or modified Schultz) index of a connected graph.
This is
$$\sum_{\{u,v\}\subseteq V} d(u)d(v)d(u,v)$$
where $d(u)$ is the degree of vertex $u$ and $d(u,v)$ is the distance between vertices $u$ and $v$.
For trees on $n$ vertices, the modified Schultz index is related to the Wiener index via $S^\ast(T)=4W(T)-(n-1)(2n-1)$ [1].
Map
subcrystal
Description
The underlying poset of the subcrystal obtained by applying the raising operators to a semistandard tableau.
Map
incomparability graph
Description
The incomparability graph of a poset.