- FindStat

Identifier

Mp00077: Semistandard tableaux —shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000970: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1],[6]] => [1,1] => [1] => [1,0,1,0] => 0

[[2],[6]] => [1,1] => [1] => [1,0,1,0] => 0

[[3],[6]] => [1,1] => [1] => [1,0,1,0] => 0

[[4],[6]] => [1,1] => [1] => [1,0,1,0] => 0

[[5],[6]] => [1,1] => [1] => [1,0,1,0] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[3,4],[5]] => [2,1] => [1] => [1,0,1,0] => 0

[[3,5],[4]] => [2,1] => [1] => [1,0,1,0] => 0

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

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

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

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

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

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

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

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

[[3],[4],[5]] => [1,1,1] => [1,1] => [1,0,1,1,0,0] => 1

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

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

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

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

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

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

>>> Load all 2039 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

Number of peaks minus the dominant dimension of the corresponding LNakayama algebra.

Map

shape

Description

Return the shape of a tableau.

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.

Map

first row removal

Description

Removes the first entry of an integer partition