Ask Your Question
0

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

asked 2022-11-11 12:45:11 +0100

lijr07 gravatar image

Let T be a semistandard tableau, for example [[1,3,5],[2,4,9]] (columns). I want to find all semistandard tableaux with the same shape and with the same content as T, which is 1,2,3,4,5,9 (the content can be a multi-set). For example, [[1,2,4],[3,5,9]] (columns) is one of such semistandard tableaux.

I can list all semistandard Young tableaux with maximal number 9:

list(SemistandardTableaux([2,2,2], max_entry=9))

and then select those with the same content as T. But this is slow when T is large. Is there faster way to do this? Thank you very much.

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted
1

answered 2022-11-12 03:40:29 +0100

Max Alekseyev gravatar image

updated 2022-11-12 03:42:21 +0100

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.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2022-11-11 12:45:11 +0100

Seen: 28 times

Last updated: Nov 12