#7301: Gale Ryser theorem
-----------------------------+----------------------------------------------
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: |
-----------------------------+----------------------------------------------
Comment(by hivert):
Hi there,
There is something I don't get in the doc:
{{{
The Gale Ryser theorem asserts that if `p_1,p_2` are two
partitions of `n` of respective lengths `k_1,k_2`, then there is
a binary `k_1\times k_2` matrix `M` such that `p_1` is the vector
of row sums and `p_2` is the vector of column sums of `M`, if
and only if `p_2` dominates `p_1`.
}}}
I suggest that the role of `p_1` and `p_2` are not symmetric... Is this
really a "if and only if" ? If you transpose the matrix then the role of
`p_1` and `p_2` are exchanged... Or dominate is not the same as dominance
order...
Am I definitely confused ???
Florent
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7301#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
