- FindStat

Identifier

Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux

Images

[[1,2]] => [[2,0],[1]] => [[1,2]]

[[2,2]] => [[2,0],[0]] => [[2,2]]

[[1],[2]] => [[1,1],[1]] => [[1],[2]]

[[1,3]] => [[2,0,0],[1,0],[1]] => [[1,3]]

[[2,3]] => [[2,0,0],[1,0],[0]] => [[2,3]]

[[3,3]] => [[2,0,0],[0,0],[0]] => [[3,3]]

[[1],[3]] => [[1,1,0],[1,0],[1]] => [[1],[3]]

[[2],[3]] => [[1,1,0],[1,0],[0]] => [[2],[3]]

[[1,1,2]] => [[3,0],[2]] => [[1,1,2]]

[[1,2,2]] => [[3,0],[1]] => [[1,2,2]]

[[2,2,2]] => [[3,0],[0]] => [[2,2,2]]

[[1,1],[2]] => [[2,1],[2]] => [[1,1],[2]]

[[1,2],[2]] => [[2,1],[1]] => [[1,2],[2]]

[[1,4]] => [[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]]

[[2,4]] => [[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]]

[[3,4]] => [[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]]

[[4,4]] => [[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]]

[[1],[4]] => [[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]]

[[2],[4]] => [[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]]

[[3],[4]] => [[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]]

[[1,1,3]] => [[3,0,0],[2,0],[2]] => [[1,1,3]]

[[1,2,3]] => [[3,0,0],[2,0],[1]] => [[1,2,3]]

[[1,3,3]] => [[3,0,0],[1,0],[1]] => [[1,3,3]]

[[2,2,3]] => [[3,0,0],[2,0],[0]] => [[2,2,3]]

[[2,3,3]] => [[3,0,0],[1,0],[0]] => [[2,3,3]]

[[3,3,3]] => [[3,0,0],[0,0],[0]] => [[3,3,3]]

[[1,1],[3]] => [[2,1,0],[2,0],[2]] => [[1,1],[3]]

[[1,2],[3]] => [[2,1,0],[2,0],[1]] => [[1,2],[3]]

[[1,3],[2]] => [[2,1,0],[1,1],[1]] => [[1,3],[2]]

[[1,3],[3]] => [[2,1,0],[1,0],[1]] => [[1,3],[3]]

[[2,2],[3]] => [[2,1,0],[2,0],[0]] => [[2,2],[3]]

[[2,3],[3]] => [[2,1,0],[1,0],[0]] => [[2,3],[3]]

[[1],[2],[3]] => [[1,1,1],[1,1],[1]] => [[1],[2],[3]]

[[1,1,1,2]] => [[4,0],[3]] => [[1,1,1,2]]

[[1,1,2,2]] => [[4,0],[2]] => [[1,1,2,2]]

[[1,2,2,2]] => [[4,0],[1]] => [[1,2,2,2]]

[[2,2,2,2]] => [[4,0],[0]] => [[2,2,2,2]]

[[1,1,1],[2]] => [[3,1],[3]] => [[1,1,1],[2]]

[[1,1,2],[2]] => [[3,1],[2]] => [[1,1,2],[2]]

[[1,2,2],[2]] => [[3,1],[1]] => [[1,2,2],[2]]

[[1,1],[2,2]] => [[2,2],[2]] => [[1,1],[2,2]]

[[1,5]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]]

[[2,5]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]]

[[3,5]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]]

[[4,5]] => [[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]]

[[5,5]] => [[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]]

[[1],[5]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]]

[[2],[5]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]]

[[3],[5]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]]

[[4],[5]] => [[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]]

[[1,1,4]] => [[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]]

[[1,2,4]] => [[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]]

[[1,3,4]] => [[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]]

[[1,4,4]] => [[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]]

[[2,2,4]] => [[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]]

[[2,3,4]] => [[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]]

[[2,4,4]] => [[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]]

[[3,3,4]] => [[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]]

[[3,4,4]] => [[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]]

[[4,4,4]] => [[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]]

[[1,1],[4]] => [[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]]

[[1,2],[4]] => [[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]]

[[1,4],[2]] => [[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]]

[[1,3],[4]] => [[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]]

[[1,4],[3]] => [[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]]

[[1,4],[4]] => [[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]]

[[2,2],[4]] => [[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]]

[[2,3],[4]] => [[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]]

[[2,4],[3]] => [[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]]

[[2,4],[4]] => [[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]]

[[3,3],[4]] => [[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]]

[[3,4],[4]] => [[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]]

[[1],[2],[4]] => [[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]]

[[1],[3],[4]] => [[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]]

[[2],[3],[4]] => [[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]]

[[1,1,1,3]] => [[4,0,0],[3,0],[3]] => [[1,1,1,3]]

[[1,1,2,3]] => [[4,0,0],[3,0],[2]] => [[1,1,2,3]]

[[1,1,3,3]] => [[4,0,0],[2,0],[2]] => [[1,1,3,3]]

[[1,2,2,3]] => [[4,0,0],[3,0],[1]] => [[1,2,2,3]]

[[1,2,3,3]] => [[4,0,0],[2,0],[1]] => [[1,2,3,3]]

[[1,3,3,3]] => [[4,0,0],[1,0],[1]] => [[1,3,3,3]]

[[2,2,2,3]] => [[4,0,0],[3,0],[0]] => [[2,2,2,3]]

[[2,2,3,3]] => [[4,0,0],[2,0],[0]] => [[2,2,3,3]]

[[2,3,3,3]] => [[4,0,0],[1,0],[0]] => [[2,3,3,3]]

[[3,3,3,3]] => [[4,0,0],[0,0],[0]] => [[3,3,3,3]]

[[1,1,1],[3]] => [[3,1,0],[3,0],[3]] => [[1,1,1],[3]]

[[1,1,2],[3]] => [[3,1,0],[3,0],[2]] => [[1,1,2],[3]]

[[1,1,3],[2]] => [[3,1,0],[2,1],[2]] => [[1,1,3],[2]]

[[1,1,3],[3]] => [[3,1,0],[2,0],[2]] => [[1,1,3],[3]]

[[1,2,2],[3]] => [[3,1,0],[3,0],[1]] => [[1,2,2],[3]]

[[1,2,3],[2]] => [[3,1,0],[2,1],[1]] => [[1,2,3],[2]]

[[1,2,3],[3]] => [[3,1,0],[2,0],[1]] => [[1,2,3],[3]]

[[1,3,3],[2]] => [[3,1,0],[1,1],[1]] => [[1,3,3],[2]]

[[1,3,3],[3]] => [[3,1,0],[1,0],[1]] => [[1,3,3],[3]]

[[2,2,2],[3]] => [[3,1,0],[3,0],[0]] => [[2,2,2],[3]]

[[2,2,3],[3]] => [[3,1,0],[2,0],[0]] => [[2,2,3],[3]]

[[2,3,3],[3]] => [[3,1,0],[1,0],[0]] => [[2,3,3],[3]]

[[1,1],[2,3]] => [[2,2,0],[2,1],[2]] => [[1,1],[2,3]]

[[1,1],[3,3]] => [[2,2,0],[2,0],[2]] => [[1,1],[3,3]]

[[1,2],[2,3]] => [[2,2,0],[2,1],[1]] => [[1,2],[2,3]]

[[1,2],[3,3]] => [[2,2,0],[2,0],[1]] => [[1,2],[3,3]]

>>> Load all 1015 entries. <<<

Map

to Gelfand-Tsetlin pattern

Description

Return the Gelfand-Tsetlin pattern corresponding to the semistandard tableau.

Map

to semistandard tableau

Description

Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let

$G$ be a Gelfand-Tsetlin pattern and let

$\lambda^{(k)}$ be its

$(n-k+1)$ -st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,

$\lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)},$
where

$\lambda^{(0)}$ is the empty partition.
Each skew shape

$\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau

$T(G)$ by inserting

$k$ into the cells of the skew shape

$\lambda^{(k)} / \lambda^{(k-1)}$ , for

$k=1,\dots,n$ .