- FindStat

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Identifier

St001686: Gelfand-Tsetlin patterns ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6,0],[4]] => 2

[[6,0],[5]] => 2

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

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

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

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

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

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

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

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

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

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

[[7,0],[0]] => 2

[[7,0],[1]] => 2

[[7,0],[2]] => 2

[[7,0],[3]] => 2

[[7,0],[4]] => 2

[[7,0],[5]] => 2

[[7,0],[6]] => 2

[[7,0],[7]] => 2

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

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

[[6,1],[3]] => 2

[[6,1],[4]] => 2

[[6,1],[5]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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]] => 1

[[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]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

$F_{(3, 2)} = 9\ q^{3}$

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

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

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

$F_{(4, 2)} = 4\ q^{2} + 12\ q^{4}$

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

$F_{(2, 5)} = 12\ q^{2}$

$F_{(3, 4)} = 33\ q^{3} + 6\ q^{6}$

$F_{(4, 3)} = 36\ q^{4} + 8\ q^{8}$

$F_{(5, 2)} = 25\ q^{5}$

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

$F_{(2, 6)} = 4\ q + 12\ q^{2}$

$F_{(3, 5)} = 51\ q^{3} + 18\ q^{6}$

$F_{(4, 4)} = 2\ q + 8\ q^{2} + 6\ q^{3} + 76\ q^{4} + 24\ q^{8}$

$F_{(5, 3)} = 65\ q^{5} + 20\ q^{10}$

$F_{(6, 2)} = 6\ q^{3} + 30\ q^{6}$

$F_{(7, 1)} = 7\ q^{7}$

$F_{(2, 7)} = 20\ q^{2}$

$F_{(3, 6)} = 5\ q + 6\ q^{2} + 78\ q^{3} + 30\ q^{6}$

$F_{(4, 5)} = 144\ q^{4} + 80\ q^{8} + 36\ q^{12}$

Description

The order of promotion on a Gelfand-Tsetlin pattern.

Code

def statistic(p):
    T = p.to_tableau()
    m = len(p)-1
    o = 1
    S = T.promotion(m)
    while S != T:
        o += 1
        S = S.promotion(m)
    return o

Created

Feb 21, 2021 at 16:58 by Martin Rubey

Updated

Feb 21, 2021 at 16:58 by Martin Rubey