#7301: Gale Ryser theorem
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Reporter: ncohen | Owner: mhansen
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3
Component: combinatorics | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by hivert):
Replying to [comment:10 wdj]:
> He is not satisfied with your implementation. He had problems with the
wording of the documentation, though he admitted this was only a minor
issue. (For example, "dominated" should be "majorized"...)
This is clearly a question of community. Those kind of matrix problem
arise in the representation theory of Symmetric Groups or in symmetric
functions and in this context I've allways seen the order called dominance
order. See eg: Macdonald, I. G. Symmetric Functions and Hall Polynomials,
2nd ed. Oxford, England: Oxford University Press, 1995.
> More important, he believed, was that the only construction implemented
was a special one (in particular, Ryser's construction was not
implemented). Without being specific, he said that more options should be
available to the user, to allow for different types of
features/constructions.
> (For example, one could allow matrices taken from another subset of
numbers, as opposed to just {0,1}.)
Again in the theory of symmetric function and descent algebra of the
symmetric group, it is useful not to give a single solution but to give
all of them, without restricting et entries of the matrix to be smaller
than one (i.e. any non negative integer). Moreover the order of the input
is important so that I'd rather have the input to be composition rather
than partition. However I don't know if in this case we need a different
enumeration algorithm. You can have a look at http://mupad-
combinat.sourceforge.net/doc/en/combinat/integerMatrices.html
to see what we had in MuPAD-Combinat.
> He was also hoping to have a construction of the graph-theoretic analog
(given a possible degree sequence, construct a graph having that degree
sequence). I presume though that, if you decided to implement that, you
would create a separate ticket.
>
> Thanks very much for working on this! I know this is a bit vague, so
please ask questions and I will ask for more details from my colleague.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7301#comment:11>
Sage <http://www.sagemath.org>
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