- FindStat

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Identifier

St000073: Gelfand-Tsetlin patterns ⟶ ℤ

Values

[[1]] => 0

[[2]] => 0

[[3]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of boxed entries.
An entry of a Gelfand-Tsetlin pattern is boxed if $a_{i,j} = a_{i-1,j-1}$ (the northwest neighbor is the same).

References

[1] Brubaker, B., Bump, D., Friedberg, S. Weyl group multiple Dirichlet series: type A combinatorial theory MathSciNet:2791904

Code

def statistic(g):
    return g.number_of_boxes()

Created

Jun 11, 2013 at 14:22 by Travis Scrimshaw

Updated

May 29, 2015 at 16:27 by Martin Rubey