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Identifier

St000173: Semistandard tableaux ⟶ ℤ

Values

[[1]] => 0

[[2]] => 1

[[3]] => 1

[[4]] => 1

[[1,1]] => 0

[[1,2]] => 1

[[2,2]] => 1

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

[[1,3]] => 1

[[2,3]] => 2

[[3,3]] => 1

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

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

[[1,4]] => 1

[[2,4]] => 2

[[3,4]] => 2

[[4,4]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The segment statistic of a semistandard tableau.
Let T be a tableau. A k-segment of T (in the ith row) is defined to be a maximal consecutive sequence of k-boxes in the ith row. Note that the possible i-boxes in the ith row are not considered to be i-segments. Then seg(T) is the total number of k-segments in T as k varies over all possible values.

References

[1] Salisbury, B. The flush statistic on semistandard Young tableaux arXiv:1401.1185

Code

def statistic(x):
    return x.seg()

Created

Jan 13, 2014 at 21:21 by Ben Salisbury

Updated

Oct 19, 2015 at 16:36 by Christian Stump