Find all semistandard Young tableaux with the same content as a given tableau.

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Here is a quick'n'dirty generator for semistandard tableaux of given shape and with given content:

def gent(shape,content,frontline=None):
    if frontline is None:
        frontline = [0] * len(shape)

    if len(content)==0:
        yield [[0]*s for s in shape]
        return

    e = content[0]
    for row,col in enumerate(frontline):
        if col>=shape[row] or (row>0 and frontline[row-1]<=col):
            continue

        frontline[row] += 1

        for t in gent(shape,content[1:],frontline):
            if row+1==len(shape) or col>=shape[row+1] or e<t[row+1][col]:
                t[row][col] = e
                yield t

        frontline[row] -= 1
    return


list(gent([3,3],[1,2,3,4,5,9]))

If given content contains duplicated elements, it may produce the same tableau several times, and so additional filtering may be needed.