#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 ncohen):
Hello everybody !!! Well, concerning the wording issue, I believe that it
is correct in this case, or that at least it depends on communities,
especially, when one looks at the code : "the conjugate of p2 dominates
p1" is written "p2.conjugate().dominates(p1), so surely I am not the only
one to give these definitions to these words :-)
The other issue seems for you to expect more than just a solution : you
are both talking about the complete enumeration of the matrices
corresponding to these criteria, and through Linear Programming I can olny
give you a simple solution, as solvers are not that bright on the
enumeration side... Would you happen to have a reference for this
algorithm ? I was onnly able to find a proof to show one matrix existed,
but nothing about enumerating them. I also have to admit that if writing
this function was quick enough because I knew what I needed and how to use
it, I may not have enough time available too look for a new ( and possibly
long ) algorithm and implement it.
Do you feel like this algorithm is totally useless as it is, or could it
be possible to take this function and create a ticket to move it to a
enumeration problem ?
Besides, your friend was talking about "different subsets of numbers".
Well, I only met this problem for 0-1 matrices and I assume your are not
talking about replacing 0 by x and 1 by y... Do you mean that there is a
version of this theorem working simultaneously for several types of
different variables (with two partitions per type of variable, etc...) ??
This would interest me very much !!
Thank you for your interest !
Nathann
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7301#comment:12>
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