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Identifier
Values
=>
Cc0019;cc-rep
[[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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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.
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
Created
Jun 02, 2019 at 23:09 by Martin Rubey
Updated
Jun 02, 2019 at 23:09 by Martin Rubey