- FindStat

Identifier

St001713: Gelfand-Tsetlin patterns ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 203 entries. <<<

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$F_{(2, 1)} = 2\ q$

$F_{(2, 2)} = 1 + 3\ q^{2}$

$F_{(3, 1)} = 3\ q$

$F_{(2, 3)} = 2\ q + 4\ q^{3}$

$F_{(3, 2)} = 3\ q + 6\ q^{2}$

$F_{(4, 1)} = 4\ q$

$F_{(2, 4)} = 1 + 3\ q^{2} + 5\ q^{4}$

$F_{(3, 3)} = 1 + 8\ q^{2} + 10\ q^{3}$

$F_{(4, 2)} = 6\ q + 10\ q^{2}$

$F_{(5, 1)} = 5\ q$

$F_{(2, 5)} = 2\ q + 4\ q^{3} + 6\ q^{5}$

$F_{(3, 4)} = 3\ q + 6\ q^{2} + 15\ q^{3} + 15\ q^{4}$

$F_{(4, 3)} = 4\ q + 20\ q^{2} + 20\ q^{3}$

$F_{(5, 2)} = 10\ q + 15\ q^{2}$

$F_{(6, 1)} = 6\ q$

Description

The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern.

Code

def statistic(G):
    return G[0][0]-G[0][-1]

Created

Apr 15, 2021 at 14:50 by Martin Rubey

Updated

Apr 15, 2021 at 14:50 by Martin Rubey