- FindStat

Identifier

Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
St000116: Semistandard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The major index of a semistandard tableau obtained by standardizing.

Map

catabolism

Description

Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).