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Statistic identifier: St001490
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Collection: Skew partitions
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Description: The number of connected components of a skew partition.
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References:
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Code:
def statistic(la):
return len(la.cell_poset().connected_components())
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Statistic values:
[[1],[]] => 1
[[2],[]] => 1
[[1,1],[]] => 1
[[2,1],[1]] => 2
[[3],[]] => 1
[[2,1],[]] => 1
[[3,1],[1]] => 2
[[2,2],[1]] => 1
[[3,2],[2]] => 2
[[1,1,1],[]] => 1
[[2,2,1],[1,1]] => 2
[[2,1,1],[1]] => 2
[[3,2,1],[2,1]] => 3
[[4],[]] => 1
[[3,1],[]] => 1
[[4,1],[1]] => 2
[[2,2],[]] => 1
[[3,2],[1]] => 1
[[4,2],[2]] => 2
[[2,1,1],[]] => 1
[[3,2,1],[1,1]] => 2
[[3,1,1],[1]] => 2
[[4,2,1],[2,1]] => 3
[[3,3],[2]] => 1
[[4,3],[3]] => 2
[[2,2,1],[1]] => 1
[[3,3,1],[2,1]] => 2
[[3,2,1],[2]] => 2
[[4,3,1],[3,1]] => 3
[[2,2,2],[1,1]] => 1
[[3,3,2],[2,2]] => 2
[[3,2,2],[2,1]] => 2
[[4,3,2],[3,2]] => 3
[[1,1,1,1],[]] => 1
[[2,2,2,1],[1,1,1]] => 2
[[2,2,1,1],[1,1]] => 2
[[3,3,2,1],[2,2,1]] => 3
[[2,1,1,1],[1]] => 2
[[3,2,2,1],[2,1,1]] => 3
[[3,2,1,1],[2,1]] => 3
[[4,3,2,1],[3,2,1]] => 4
[[5],[]] => 1
[[4,1],[]] => 1
[[5,1],[1]] => 2
[[3,2],[]] => 1
[[4,2],[1]] => 1
[[5,2],[2]] => 2
[[3,1,1],[]] => 1
[[4,2,1],[1,1]] => 2
[[4,1,1],[1]] => 2
[[5,2,1],[2,1]] => 3
[[3,3],[1]] => 1
[[4,3],[2]] => 1
[[5,3],[3]] => 2
[[2,2,1],[]] => 1
[[3,3,1],[1,1]] => 2
[[3,2,1],[1]] => 1
[[4,3,1],[2,1]] => 2
[[4,2,1],[2]] => 2
[[5,3,1],[3,1]] => 3
[[3,2,2],[1,1]] => 1
[[4,3,2],[2,2]] => 2
[[4,2,2],[2,1]] => 2
[[5,3,2],[3,2]] => 3
[[2,1,1,1],[]] => 1
[[3,2,2,1],[1,1,1]] => 2
[[3,2,1,1],[1,1]] => 2
[[4,3,2,1],[2,2,1]] => 3
[[3,1,1,1],[1]] => 2
[[4,2,2,1],[2,1,1]] => 3
[[4,2,1,1],[2,1]] => 3
[[5,3,2,1],[3,2,1]] => 4
[[4,4],[3]] => 1
[[5,4],[4]] => 2
[[3,3,1],[2]] => 1
[[4,4,1],[3,1]] => 2
[[4,3,1],[3]] => 2
[[5,4,1],[4,1]] => 3
[[2,2,2],[1]] => 1
[[3,3,2],[2,1]] => 1
[[4,4,2],[3,2]] => 2
[[3,2,2],[2]] => 2
[[4,3,2],[3,1]] => 2
[[5,4,2],[4,2]] => 3
[[2,2,1,1],[1]] => 1
[[3,3,2,1],[2,1,1]] => 2
[[3,3,1,1],[2,1]] => 2
[[4,4,2,1],[3,2,1]] => 3
[[3,2,1,1],[2]] => 2
[[4,3,2,1],[3,1,1]] => 3
[[4,3,1,1],[3,1]] => 3
[[5,4,2,1],[4,2,1]] => 4
[[3,3,3],[2,2]] => 1
[[4,4,3],[3,3]] => 2
[[4,3,3],[3,2]] => 2
[[5,4,3],[4,3]] => 3
[[2,2,2,1],[1,1]] => 1
[[3,3,3,1],[2,2,1]] => 2
[[3,3,2,1],[2,2]] => 2
[[4,4,3,1],[3,3,1]] => 3
[[3,2,2,1],[2,1]] => 2
[[4,3,3,1],[3,2,1]] => 3
[[4,3,2,1],[3,2]] => 3
[[5,4,3,1],[4,3,1]] => 4
[[2,2,2,2],[1,1,1]] => 1
[[3,3,3,2],[2,2,2]] => 2
[[3,3,2,2],[2,2,1]] => 2
[[4,4,3,2],[3,3,2]] => 3
[[3,2,2,2],[2,1,1]] => 2
[[4,3,3,2],[3,2,2]] => 3
[[4,3,2,2],[3,2,1]] => 3
[[5,4,3,2],[4,3,2]] => 4
[[1,1,1,1,1],[]] => 1
[[2,2,2,2,1],[1,1,1,1]] => 2
[[2,2,2,1,1],[1,1,1]] => 2
[[3,3,3,2,1],[2,2,2,1]] => 3
[[2,2,1,1,1],[1,1]] => 2
[[3,3,2,2,1],[2,2,1,1]] => 3
[[3,3,2,1,1],[2,2,1]] => 3
[[4,4,3,2,1],[3,3,2,1]] => 4
[[2,1,1,1,1],[1]] => 2
[[3,2,2,2,1],[2,1,1,1]] => 3
[[3,2,2,1,1],[2,1,1]] => 3
[[4,3,3,2,1],[3,2,2,1]] => 4
[[3,2,1,1,1],[2,1]] => 3
[[4,3,2,2,1],[3,2,1,1]] => 4
[[4,3,2,1,1],[3,2,1]] => 4
[[5,4,3,2,1],[4,3,2,1]] => 5
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Created: Oct 30, 2019 at 12:59 by Martin Rubey
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Last Updated: Oct 30, 2019 at 12:59 by Martin Rubey