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Statistic identifier: St001407
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Collection: Semistandard tableaux
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Description: The number of minimal entries in a semistandard tableau.
An entry is minimal if replacing it with a smaller entry does not yield a semistandard tableau.
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References:
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Code:
def statistic(T):
S = [[e for e in row] for row in T]
count = 0
for i, row in enumerate(S):
for j, e in enumerate(row):
S[i][j] = e-1
try:
_ = SemistandardTableau(S)
except StandardError:
count += 1
S[i][j] = e
return count
-----------------------------------------------------------------------------
Statistic values:
[[1,2]] => 1
[[2,2]] => 1
[[1],[2]] => 2
[[1,3]] => 1
[[2,3]] => 0
[[3,3]] => 1
[[1],[3]] => 1
[[2],[3]] => 1
[[1,4]] => 1
[[2,4]] => 0
[[3,4]] => 0
[[4,4]] => 1
[[1],[4]] => 1
[[2],[4]] => 0
[[3],[4]] => 1
[[1,5]] => 1
[[2,5]] => 0
[[3,5]] => 0
[[4,5]] => 0
[[5,5]] => 1
[[1],[5]] => 1
[[2],[5]] => 0
[[3],[5]] => 0
[[4],[5]] => 1
[[1,6]] => 1
[[2,6]] => 0
[[3,6]] => 0
[[4,6]] => 0
[[5,6]] => 0
[[6,6]] => 1
[[1],[6]] => 1
[[2],[6]] => 0
[[3],[6]] => 0
[[4],[6]] => 0
[[5],[6]] => 1
[[1,1,2]] => 2
[[1,2,2]] => 2
[[2,2,2]] => 2
[[1,1],[2]] => 3
[[1,2],[2]] => 2
[[1,1,3]] => 2
[[1,2,3]] => 1
[[1,3,3]] => 2
[[2,2,3]] => 1
[[2,3,3]] => 1
[[3,3,3]] => 2
[[1,1],[3]] => 2
[[1,2],[3]] => 1
[[1,3],[2]] => 2
[[1,3],[3]] => 1
[[2,2],[3]] => 2
[[2,3],[3]] => 1
[[1],[2],[3]] => 3
[[1,1,4]] => 2
[[1,2,4]] => 1
[[1,3,4]] => 1
[[1,4,4]] => 2
[[2,2,4]] => 1
[[2,3,4]] => 0
[[2,4,4]] => 1
[[3,3,4]] => 1
[[3,4,4]] => 1
[[4,4,4]] => 2
[[1,1],[4]] => 2
[[1,2],[4]] => 1
[[1,4],[2]] => 2
[[1,3],[4]] => 1
[[1,4],[3]] => 1
[[1,4],[4]] => 1
[[2,2],[4]] => 1
[[2,3],[4]] => 0
[[2,4],[3]] => 1
[[2,4],[4]] => 0
[[3,3],[4]] => 2
[[3,4],[4]] => 1
[[1],[2],[4]] => 2
[[1],[3],[4]] => 2
[[2],[3],[4]] => 2
[[1,1,5]] => 2
[[1,2,5]] => 1
[[1,3,5]] => 1
[[1,4,5]] => 1
[[1,5,5]] => 2
[[2,2,5]] => 1
[[2,3,5]] => 0
[[2,4,5]] => 0
[[2,5,5]] => 1
[[3,3,5]] => 1
[[3,4,5]] => 0
[[3,5,5]] => 1
[[4,4,5]] => 1
[[4,5,5]] => 1
[[5,5,5]] => 2
[[1,1],[5]] => 2
[[1,2],[5]] => 1
[[1,5],[2]] => 2
[[1,3],[5]] => 1
[[1,5],[3]] => 1
[[1,4],[5]] => 1
[[1,5],[4]] => 1
[[1,5],[5]] => 1
[[2,2],[5]] => 1
[[2,3],[5]] => 0
[[2,5],[3]] => 1
[[2,4],[5]] => 0
[[2,5],[4]] => 0
[[2,5],[5]] => 0
[[3,3],[5]] => 1
[[3,4],[5]] => 0
[[3,5],[4]] => 1
[[3,5],[5]] => 0
[[4,4],[5]] => 2
[[4,5],[5]] => 1
[[1],[2],[5]] => 2
[[1],[3],[5]] => 1
[[1],[4],[5]] => 2
[[2],[3],[5]] => 1
[[2],[4],[5]] => 1
[[3],[4],[5]] => 2
[[1,1,1,2]] => 3
[[1,1,2,2]] => 3
[[1,2,2,2]] => 3
[[2,2,2,2]] => 3
[[1,1,1],[2]] => 4
[[1,1,2],[2]] => 3
[[1,2,2],[2]] => 3
[[1,1],[2,2]] => 4
[[1,1,1,3]] => 3
[[1,1,2,3]] => 2
[[1,1,3,3]] => 3
[[1,2,2,3]] => 2
[[1,2,3,3]] => 2
[[1,3,3,3]] => 3
[[2,2,2,3]] => 2
[[2,2,3,3]] => 2
[[2,3,3,3]] => 2
[[3,3,3,3]] => 3
[[1,1,1],[3]] => 3
[[1,1,2],[3]] => 2
[[1,1,3],[2]] => 3
[[1,1,3],[3]] => 2
[[1,2,2],[3]] => 2
[[1,2,3],[2]] => 2
[[1,2,3],[3]] => 1
[[1,3,3],[2]] => 3
[[1,3,3],[3]] => 2
[[2,2,2],[3]] => 3
[[2,2,3],[3]] => 2
[[2,3,3],[3]] => 2
[[1,1],[2,3]] => 3
[[1,1],[3,3]] => 3
[[1,2],[2,3]] => 3
[[1,2],[3,3]] => 2
[[2,2],[3,3]] => 3
[[1,1],[2],[3]] => 4
[[1,2],[2],[3]] => 3
[[1,3],[2],[3]] => 3
[[1,1,1,4]] => 3
[[1,1,2,4]] => 2
[[1,1,3,4]] => 2
[[1,1,4,4]] => 3
[[1,2,2,4]] => 2
[[1,2,3,4]] => 1
[[1,2,4,4]] => 2
[[1,3,3,4]] => 2
[[1,3,4,4]] => 2
[[1,4,4,4]] => 3
[[2,2,2,4]] => 2
[[2,2,3,4]] => 1
[[2,2,4,4]] => 2
[[2,3,3,4]] => 1
[[2,3,4,4]] => 1
[[2,4,4,4]] => 2
[[3,3,3,4]] => 2
[[3,3,4,4]] => 2
[[3,4,4,4]] => 2
[[4,4,4,4]] => 3
[[1,1,1],[4]] => 3
[[1,1,2],[4]] => 2
[[1,1,4],[2]] => 3
[[1,1,3],[4]] => 2
[[1,1,4],[3]] => 2
[[1,1,4],[4]] => 2
[[1,2,2],[4]] => 2
[[1,2,4],[2]] => 2
[[1,2,3],[4]] => 1
[[1,2,4],[3]] => 1
[[1,3,4],[2]] => 2
[[1,2,4],[4]] => 1
[[1,4,4],[2]] => 3
[[1,3,3],[4]] => 2
[[1,3,4],[3]] => 1
[[1,3,4],[4]] => 1
[[1,4,4],[3]] => 2
[[1,4,4],[4]] => 2
[[2,2,2],[4]] => 2
[[2,2,3],[4]] => 1
[[2,2,4],[3]] => 2
[[2,2,4],[4]] => 1
[[2,3,3],[4]] => 1
[[2,3,4],[3]] => 1
[[2,3,4],[4]] => 0
[[2,4,4],[3]] => 2
[[2,4,4],[4]] => 1
[[3,3,3],[4]] => 3
[[3,3,4],[4]] => 2
[[3,4,4],[4]] => 2
[[1,1],[2,4]] => 3
[[1,1],[3,4]] => 2
[[1,1],[4,4]] => 3
[[1,2],[2,4]] => 2
[[1,2],[3,4]] => 1
[[1,3],[2,4]] => 3
[[1,2],[4,4]] => 2
[[1,3],[3,4]] => 2
[[1,3],[4,4]] => 2
[[2,2],[3,4]] => 2
[[2,2],[4,4]] => 2
[[2,3],[3,4]] => 2
[[2,3],[4,4]] => 1
[[3,3],[4,4]] => 3
[[1,1],[2],[4]] => 3
[[1,1],[3],[4]] => 3
[[1,2],[2],[4]] => 2
[[1,2],[3],[4]] => 2
[[1,3],[2],[4]] => 2
[[1,4],[2],[3]] => 3
[[1,4],[2],[4]] => 2
[[1,3],[3],[4]] => 2
[[1,4],[3],[4]] => 2
[[2,2],[3],[4]] => 3
[[2,3],[3],[4]] => 2
[[2,4],[3],[4]] => 2
[[1],[2],[3],[4]] => 4
[[1,1,1,1,2]] => 4
[[1,1,1,2,2]] => 4
[[1,1,2,2,2]] => 4
[[1,2,2,2,2]] => 4
[[2,2,2,2,2]] => 4
[[1,1,1,1],[2]] => 5
[[1,1,1,2],[2]] => 4
[[1,1,2,2],[2]] => 4
[[1,2,2,2],[2]] => 4
[[1,1,1],[2,2]] => 5
[[1,1,2],[2,2]] => 4
[[1,1,1,1,3]] => 4
[[1,1,1,2,3]] => 3
[[1,1,1,3,3]] => 4
[[1,1,2,2,3]] => 3
[[1,1,2,3,3]] => 3
[[1,1,3,3,3]] => 4
[[1,2,2,2,3]] => 3
[[1,2,2,3,3]] => 3
[[1,2,3,3,3]] => 3
[[1,3,3,3,3]] => 4
[[2,2,2,2,3]] => 3
[[2,2,2,3,3]] => 3
[[2,2,3,3,3]] => 3
[[2,3,3,3,3]] => 3
[[3,3,3,3,3]] => 4
[[1,1,1,1],[3]] => 4
[[1,1,1,2],[3]] => 3
[[1,1,1,3],[2]] => 4
[[1,1,1,3],[3]] => 3
[[1,1,2,2],[3]] => 3
[[1,1,2,3],[2]] => 3
[[1,1,2,3],[3]] => 2
[[1,1,3,3],[2]] => 4
[[1,1,3,3],[3]] => 3
[[1,2,2,2],[3]] => 3
[[1,2,2,3],[2]] => 3
[[1,2,2,3],[3]] => 2
[[1,2,3,3],[2]] => 3
[[1,2,3,3],[3]] => 2
[[1,3,3,3],[2]] => 4
[[1,3,3,3],[3]] => 3
[[2,2,2,2],[3]] => 4
[[2,2,2,3],[3]] => 3
[[2,2,3,3],[3]] => 3
[[2,3,3,3],[3]] => 3
[[1,1,1],[2,3]] => 4
[[1,1,1],[3,3]] => 4
[[1,1,2],[2,3]] => 3
[[1,1,3],[2,2]] => 4
[[1,1,2],[3,3]] => 3
[[1,1,3],[2,3]] => 3
[[1,1,3],[3,3]] => 3
[[1,2,2],[2,3]] => 4
[[1,2,2],[3,3]] => 3
[[1,2,3],[2,3]] => 3
[[1,2,3],[3,3]] => 2
[[2,2,2],[3,3]] => 4
[[2,2,3],[3,3]] => 3
[[1,1,1],[2],[3]] => 5
[[1,1,2],[2],[3]] => 4
[[1,1,3],[2],[3]] => 4
[[1,2,2],[2],[3]] => 4
[[1,2,3],[2],[3]] => 3
[[1,3,3],[2],[3]] => 4
[[1,1],[2,2],[3]] => 5
[[1,1],[2,3],[3]] => 4
[[1,2],[2,3],[3]] => 4
[[1,1,1,1,1,2]] => 5
[[1,1,1,1,2,2]] => 5
[[1,1,1,2,2,2]] => 5
[[1,1,2,2,2,2]] => 5
[[1,2,2,2,2,2]] => 5
[[2,2,2,2,2,2]] => 5
[[1,1,1,1,1],[2]] => 6
[[1,1,1,1,2],[2]] => 5
[[1,1,1,2,2],[2]] => 5
[[1,1,2,2,2],[2]] => 5
[[1,2,2,2,2],[2]] => 5
[[1,1,1,1],[2,2]] => 6
[[1,1,1,2],[2,2]] => 5
[[1,1,2,2],[2,2]] => 5
[[1,1,1],[2,2,2]] => 6
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Created: Jun 02, 2019 at 23:09 by Martin Rubey
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Last Updated: Jun 02, 2019 at 23:09 by Martin Rubey