Identifier
Identifier
Values
[[1,2]] generating graphics... => 1
[[2,2]] generating graphics... => 1
[[1],[2]] generating graphics... => 2
[[1,3]] generating graphics... => 1
[[2,3]] generating graphics... => 0
[[3,3]] generating graphics... => 1
[[1],[3]] generating graphics... => 1
[[2],[3]] generating graphics... => 1
[[1,4]] generating graphics... => 1
[[2,4]] generating graphics... => 0
[[3,4]] generating graphics... => 0
[[4,4]] generating graphics... => 1
[[1],[4]] generating graphics... => 1
[[2],[4]] generating graphics... => 0
[[3],[4]] generating graphics... => 1
[[1,5]] generating graphics... => 1
[[2,5]] generating graphics... => 0
[[3,5]] generating graphics... => 0
[[4,5]] generating graphics... => 0
[[5,5]] generating graphics... => 1
[[1],[5]] generating graphics... => 1
[[2],[5]] generating graphics... => 0
[[3],[5]] generating graphics... => 0
[[4],[5]] generating graphics... => 1
[[1,6]] generating graphics... => 1
[[2,6]] generating graphics... => 0
[[3,6]] generating graphics... => 0
[[4,6]] generating graphics... => 0
[[5,6]] generating graphics... => 0
[[6,6]] generating graphics... => 1
[[1],[6]] generating graphics... => 1
[[2],[6]] generating graphics... => 0
[[3],[6]] generating graphics... => 0
[[4],[6]] generating graphics... => 0
[[5],[6]] generating graphics... => 1
[[1,1,2]] generating graphics... => 2
[[1,2,2]] generating graphics... => 2
[[2,2,2]] generating graphics... => 2
[[1,1],[2]] generating graphics... => 3
[[1,2],[2]] generating graphics... => 2
[[1,1,3]] generating graphics... => 2
[[1,2,3]] generating graphics... => 1
[[1,3,3]] generating graphics... => 2
[[2,2,3]] generating graphics... => 1
[[2,3,3]] generating graphics... => 1
[[3,3,3]] generating graphics... => 2
[[1,1],[3]] generating graphics... => 2
[[1,2],[3]] generating graphics... => 1
[[1,3],[2]] generating graphics... => 2
[[1,3],[3]] generating graphics... => 1
[[2,2],[3]] generating graphics... => 2
[[2,3],[3]] generating graphics... => 1
[[1],[2],[3]] generating graphics... => 3
[[1,1,4]] generating graphics... => 2
[[1,2,4]] generating graphics... => 1
[[1,3,4]] generating graphics... => 1
[[1,4,4]] generating graphics... => 2
[[2,2,4]] generating graphics... => 1
[[2,3,4]] generating graphics... => 0
[[2,4,4]] generating graphics... => 1
[[3,3,4]] generating graphics... => 1
[[3,4,4]] generating graphics... => 1
[[4,4,4]] generating graphics... => 2
[[1,1],[4]] generating graphics... => 2
[[1,2],[4]] generating graphics... => 1
[[1,4],[2]] generating graphics... => 2
[[1,3],[4]] generating graphics... => 1
[[1,4],[3]] generating graphics... => 1
[[1,4],[4]] generating graphics... => 1
[[2,2],[4]] generating graphics... => 1
[[2,3],[4]] generating graphics... => 0
[[2,4],[3]] generating graphics... => 1
[[2,4],[4]] generating graphics... => 0
[[3,3],[4]] generating graphics... => 2
[[3,4],[4]] generating graphics... => 1
[[1],[2],[4]] generating graphics... => 2
[[1],[3],[4]] generating graphics... => 2
[[2],[3],[4]] generating graphics... => 2
[[1,1,5]] generating graphics... => 2
[[1,2,5]] generating graphics... => 1
[[1,3,5]] generating graphics... => 1
[[1,4,5]] generating graphics... => 1
[[1,5,5]] generating graphics... => 2
[[2,2,5]] generating graphics... => 1
[[2,3,5]] generating graphics... => 0
[[2,4,5]] generating graphics... => 0
[[2,5,5]] generating graphics... => 1
[[3,3,5]] generating graphics... => 1
[[3,4,5]] generating graphics... => 0
[[3,5,5]] generating graphics... => 1
[[4,4,5]] generating graphics... => 1
[[4,5,5]] generating graphics... => 1
[[5,5,5]] generating graphics... => 2
[[1,1],[5]] generating graphics... => 2
[[1,2],[5]] generating graphics... => 1
[[1,5],[2]] generating graphics... => 2
[[1,3],[5]] generating graphics... => 1
[[1,5],[3]] generating graphics... => 1
[[1,4],[5]] generating graphics... => 1
[[1,5],[4]] generating graphics... => 1
[[1,5],[5]] generating graphics... => 1
[[2,2],[5]] generating graphics... => 1
[[2,3],[5]] generating graphics... => 0
[[2,5],[3]] generating graphics... => 1
[[2,4],[5]] generating graphics... => 0
[[2,5],[4]] generating graphics... => 0
[[2,5],[5]] generating graphics... => 0
[[3,3],[5]] generating graphics... => 1
[[3,4],[5]] generating graphics... => 0
[[3,5],[4]] generating graphics... => 1
[[3,5],[5]] generating graphics... => 0
[[4,4],[5]] generating graphics... => 2
[[4,5],[5]] generating graphics... => 1
[[1],[2],[5]] generating graphics... => 2
[[1],[3],[5]] generating graphics... => 1
[[1],[4],[5]] generating graphics... => 2
[[2],[3],[5]] generating graphics... => 1
[[2],[4],[5]] generating graphics... => 1
[[3],[4],[5]] generating graphics... => 2
[[1,1,1,2]] generating graphics... => 3
[[1,1,2,2]] generating graphics... => 3
[[1,2,2,2]] generating graphics... => 3
[[2,2,2,2]] generating graphics... => 3
[[1,1,1],[2]] generating graphics... => 4
[[1,1,2],[2]] generating graphics... => 3
[[1,2,2],[2]] generating graphics... => 3
[[1,1],[2,2]] generating graphics... => 4
[[1,1,1,3]] generating graphics... => 3
[[1,1,2,3]] generating graphics... => 2
[[1,1,3,3]] generating graphics... => 3
[[1,2,2,3]] generating graphics... => 2
[[1,2,3,3]] generating graphics... => 2
[[1,3,3,3]] generating graphics... => 3
[[2,2,2,3]] generating graphics... => 2
[[2,2,3,3]] generating graphics... => 2
[[2,3,3,3]] generating graphics... => 2
[[3,3,3,3]] generating graphics... => 3
[[1,1,1],[3]] generating graphics... => 3
[[1,1,2],[3]] generating graphics... => 2
[[1,1,3],[2]] generating graphics... => 3
[[1,1,3],[3]] generating graphics... => 2
[[1,2,2],[3]] generating graphics... => 2
[[1,2,3],[2]] generating graphics... => 2
[[1,2,3],[3]] generating graphics... => 1
[[1,3,3],[2]] generating graphics... => 3
[[1,3,3],[3]] generating graphics... => 2
[[2,2,2],[3]] generating graphics... => 3
[[2,2,3],[3]] generating graphics... => 2
[[2,3,3],[3]] generating graphics... => 2
[[1,1],[2,3]] generating graphics... => 3
[[1,1],[3,3]] generating graphics... => 3
[[1,2],[2,3]] generating graphics... => 3
[[1,2],[3,3]] generating graphics... => 2
[[2,2],[3,3]] generating graphics... => 3
[[1,1],[2],[3]] generating graphics... => 4
[[1,2],[2],[3]] generating graphics... => 3
[[1,3],[2],[3]] generating graphics... => 3
[[1,1,1,4]] generating graphics... => 3
[[1,1,2,4]] generating graphics... => 2
[[1,1,3,4]] generating graphics... => 2
[[1,1,4,4]] generating graphics... => 3
[[1,2,2,4]] generating graphics... => 2
[[1,2,3,4]] generating graphics... => 1
[[1,2,4,4]] generating graphics... => 2
[[1,3,3,4]] generating graphics... => 2
[[1,3,4,4]] generating graphics... => 2
[[1,4,4,4]] generating graphics... => 3
[[2,2,2,4]] generating graphics... => 2
[[2,2,3,4]] generating graphics... => 1
[[2,2,4,4]] generating graphics... => 2
[[2,3,3,4]] generating graphics... => 1
[[2,3,4,4]] generating graphics... => 1
[[2,4,4,4]] generating graphics... => 2
[[3,3,3,4]] generating graphics... => 2
[[3,3,4,4]] generating graphics... => 2
[[3,4,4,4]] generating graphics... => 2
[[4,4,4,4]] generating graphics... => 3
[[1,1,1],[4]] generating graphics... => 3
[[1,1,2],[4]] generating graphics... => 2
[[1,1,4],[2]] generating graphics... => 3
[[1,1,3],[4]] generating graphics... => 2
[[1,1,4],[3]] generating graphics... => 2
[[1,1,4],[4]] generating graphics... => 2
[[1,2,2],[4]] generating graphics... => 2
[[1,2,4],[2]] generating graphics... => 2
[[1,2,3],[4]] generating graphics... => 1
[[1,2,4],[3]] generating graphics... => 1
[[1,3,4],[2]] generating graphics... => 2
[[1,2,4],[4]] generating graphics... => 1
[[1,4,4],[2]] generating graphics... => 3
[[1,3,3],[4]] generating graphics... => 2
[[1,3,4],[3]] generating graphics... => 1
[[1,3,4],[4]] generating graphics... => 1
[[1,4,4],[3]] generating graphics... => 2
[[1,4,4],[4]] generating graphics... => 2
[[2,2,2],[4]] generating graphics... => 2
[[2,2,3],[4]] generating graphics... => 1
[[2,2,4],[3]] generating graphics... => 2
[[2,2,4],[4]] generating graphics... => 1
[[2,3,3],[4]] generating graphics... => 1
[[2,3,4],[3]] generating graphics... => 1
[[2,3,4],[4]] generating graphics... => 0
[[2,4,4],[3]] generating graphics... => 2
[[2,4,4],[4]] generating graphics... => 1
[[3,3,3],[4]] generating graphics... => 3
[[3,3,4],[4]] generating graphics... => 2
[[3,4,4],[4]] generating graphics... => 2
[[1,1],[2,4]] generating graphics... => 3
[[1,1],[3,4]] generating graphics... => 2
[[1,1],[4,4]] generating graphics... => 3
[[1,2],[2,4]] generating graphics... => 2
[[1,2],[3,4]] generating graphics... => 1
[[1,3],[2,4]] generating graphics... => 3
[[1,2],[4,4]] generating graphics... => 2
[[1,3],[3,4]] generating graphics... => 2
[[1,3],[4,4]] generating graphics... => 2
[[2,2],[3,4]] generating graphics... => 2
[[2,2],[4,4]] generating graphics... => 2
[[2,3],[3,4]] generating graphics... => 2
[[2,3],[4,4]] generating graphics... => 1
[[3,3],[4,4]] generating graphics... => 3
[[1,1],[2],[4]] generating graphics... => 3
[[1,1],[3],[4]] generating graphics... => 3
[[1,2],[2],[4]] generating graphics... => 2
[[1,2],[3],[4]] generating graphics... => 2
[[1,3],[2],[4]] generating graphics... => 2
[[1,4],[2],[3]] generating graphics... => 3
[[1,4],[2],[4]] generating graphics... => 2
[[1,3],[3],[4]] generating graphics... => 2
[[1,4],[3],[4]] generating graphics... => 2
[[2,2],[3],[4]] generating graphics... => 3
[[2,3],[3],[4]] generating graphics... => 2
[[2,4],[3],[4]] generating graphics... => 2
[[1],[2],[3],[4]] generating graphics... => 4
[[1,1,1,1,2]] generating graphics... => 4
[[1,1,1,2,2]] generating graphics... => 4
[[1,1,2,2,2]] generating graphics... => 4
[[1,2,2,2,2]] generating graphics... => 4
[[2,2,2,2,2]] generating graphics... => 4
[[1,1,1,1],[2]] generating graphics... => 5
[[1,1,1,2],[2]] generating graphics... => 4
[[1,1,2,2],[2]] generating graphics... => 4
[[1,2,2,2],[2]] generating graphics... => 4
[[1,1,1],[2,2]] generating graphics... => 5
[[1,1,2],[2,2]] generating graphics... => 4
[[1,1,1,1,3]] generating graphics... => 4
[[1,1,1,2,3]] generating graphics... => 3
[[1,1,1,3,3]] generating graphics... => 4
[[1,1,2,2,3]] generating graphics... => 3
[[1,1,2,3,3]] generating graphics... => 3
[[1,1,3,3,3]] generating graphics... => 4
[[1,2,2,2,3]] generating graphics... => 3
[[1,2,2,3,3]] generating graphics... => 3
[[1,2,3,3,3]] generating graphics... => 3
[[1,3,3,3,3]] generating graphics... => 4
[[2,2,2,2,3]] generating graphics... => 3
[[2,2,2,3,3]] generating graphics... => 3
[[2,2,3,3,3]] generating graphics... => 3
[[2,3,3,3,3]] generating graphics... => 3
[[3,3,3,3,3]] generating graphics... => 4
[[1,1,1,1],[3]] generating graphics... => 4
[[1,1,1,2],[3]] generating graphics... => 3
[[1,1,1,3],[2]] generating graphics... => 4
[[1,1,1,3],[3]] generating graphics... => 3
[[1,1,2,2],[3]] generating graphics... => 3
[[1,1,2,3],[2]] generating graphics... => 3
[[1,1,2,3],[3]] generating graphics... => 2
[[1,1,3,3],[2]] generating graphics... => 4
[[1,1,3,3],[3]] generating graphics... => 3
[[1,2,2,2],[3]] generating graphics... => 3
[[1,2,2,3],[2]] generating graphics... => 3
[[1,2,2,3],[3]] generating graphics... => 2
[[1,2,3,3],[2]] generating graphics... => 3
[[1,2,3,3],[3]] generating graphics... => 2
[[1,3,3,3],[2]] generating graphics... => 4
[[1,3,3,3],[3]] generating graphics... => 3
[[2,2,2,2],[3]] generating graphics... => 4
[[2,2,2,3],[3]] generating graphics... => 3
[[2,2,3,3],[3]] generating graphics... => 3
[[2,3,3,3],[3]] generating graphics... => 3
[[1,1,1],[2,3]] generating graphics... => 4
[[1,1,1],[3,3]] generating graphics... => 4
[[1,1,2],[2,3]] generating graphics... => 3
[[1,1,3],[2,2]] generating graphics... => 4
[[1,1,2],[3,3]] generating graphics... => 3
[[1,1,3],[2,3]] generating graphics... => 3
[[1,1,3],[3,3]] generating graphics... => 3
[[1,2,2],[2,3]] generating graphics... => 4
[[1,2,2],[3,3]] generating graphics... => 3
[[1,2,3],[2,3]] generating graphics... => 3
[[1,2,3],[3,3]] generating graphics... => 2
[[2,2,2],[3,3]] generating graphics... => 4
[[2,2,3],[3,3]] generating graphics... => 3
[[1,1,1],[2],[3]] generating graphics... => 5
[[1,1,2],[2],[3]] generating graphics... => 4
[[1,1,3],[2],[3]] generating graphics... => 4
[[1,2,2],[2],[3]] generating graphics... => 4
[[1,2,3],[2],[3]] generating graphics... => 3
[[1,3,3],[2],[3]] generating graphics... => 4
[[1,1],[2,2],[3]] generating graphics... => 5
[[1,1],[2,3],[3]] generating graphics... => 4
[[1,2],[2,3],[3]] generating graphics... => 4
[[1,1,1,1,1,2]] generating graphics... => 5
[[1,1,1,1,2,2]] generating graphics... => 5
[[1,1,1,2,2,2]] generating graphics... => 5
[[1,1,2,2,2,2]] generating graphics... => 5
[[1,2,2,2,2,2]] generating graphics... => 5
[[2,2,2,2,2,2]] generating graphics... => 5
[[1,1,1,1,1],[2]] generating graphics... => 6
[[1,1,1,1,2],[2]] generating graphics... => 5
[[1,1,1,2,2],[2]] generating graphics... => 5
[[1,1,2,2,2],[2]] generating graphics... => 5
[[1,2,2,2,2],[2]] generating graphics... => 5
[[1,1,1,1],[2,2]] generating graphics... => 6
[[1,1,1,2],[2,2]] generating graphics... => 5
[[1,1,2,2],[2,2]] generating graphics... => 5
[[1,1,1],[2,2,2]] generating graphics... => 6
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