- FindStat

edit this statistic or download as text // json

Identifier

St000116: Semistandard tableaux ⟶ ℤ

Values

[[1]] => 0

[[2]] => 0

[[3]] => 0

[[4]] => 0

[[1,1]] => 0

[[1,2]] => 0

[[2,2]] => 0

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

[[1,3]] => 0

[[2,3]] => 0

[[3,3]] => 0

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

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

[[1,4]] => 0

[[2,4]] => 0

[[3,4]] => 0

[[4,4]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1189 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The major index of a semistandard tableau obtained by standardizing.

Code

def statistic(t):
    return Permutation(t.standardization().to_word()).major_index()

Created

Jun 17, 2013 at 23:45 by Anne Schilling

Updated

Oct 19, 2015 at 16:36 by Christian Stump