- FindStat

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Identifier

St000077: Gelfand-Tsetlin patterns ⟶ ℤ

Values

[[1]] => 0

[[2]] => 0

[[3]] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[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]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of boxed and circled entries.
An entry $a_{i,j}$ is boxed and circled if $a_{i-1,j-i} = a_{i,j} = a_{i-1,j}$.

Code

def statistic(g):
    boxed = g.boxed_entries()
    return sum(1 for x in g.circled_entries() if x in boxed)

Created

Jun 11, 2013 at 18:28 by Travis Scrimshaw

Updated

Apr 01, 2015 at 21:33 by Martin Rubey