Timeline for Minimal possible cardinality of a $(a_1, ..., a_k)$-distributable multiset
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| May 4, 2019 at 10:47 | answer | added | Fedor Petrov | timeline score: 3 | |
| Feb 13, 2018 at 23:31 | comment | added | Gerry Myerson | See also oeis.org/A265286 | |
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Dec 5, 2015 at 1:31 | answer | added | Max Alekseyev | timeline score: 4 | |
| Aug 12, 2015 at 2:42 | comment | added | Brendan McKay | Note that these are the central transportation polytopes. For dimensions greater than 2, I'm not sure if there is a description of the vertices useful for this problem. | |
| Aug 12, 2015 at 1:44 | comment | added | Brendan McKay | @Dennis : Consider the case $(3,4)$ for illustration. Any solution has the form of a $3\times 4$ matrix of nonnegative rational (might as well be real) numbers with row sums $1/3$ and column sums $1/4$. Such matrices form a convex polytope defined by the row/column sums and the nonnegativity. The problem is to minimise the number of nonnegative entries, i.e. to maximise the number of zero entries. I think (is it obvious?) that this maximum occurs at some vertex of the polytope but I don't know how to find that vertex. | |
| Aug 11, 2015 at 12:28 | comment | added | Glinka | @BrendanMcKay, could you please explain your idea more extensively? | |
| Aug 11, 2015 at 1:04 | comment | added | Brendan McKay | @Gerry: Thanks. It seems we are seeking a vertex of a polytope that has the greatest number of zero components. Investigating the polytope combinatorially might be productive. | |
| Aug 11, 2015 at 0:10 | comment | added | Gerry Myerson | @Brendan, non-triviality is in the eye of the beholder, but there are some examples at the second math.stackexchange link. In particular, I sketch an argument that $(3,4,n)$, for $\gcd(n,6)=1$, can be done $M=n+4$, and I give a couple of other examples. My $(3,4,n)$ is based on the $(3,4,5)$ example at the first math.stackexchange link. | |
| Aug 10, 2015 at 22:52 | comment | added | Brendan McKay | A nontrivial example would add motivation.. | |
| Aug 10, 2015 at 21:02 | history | edited | Glinka | CC BY-SA 3.0 |
deleted 2 characters in body
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| Aug 10, 2015 at 20:57 | review | First posts | |||
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| Aug 10, 2015 at 20:56 | history | asked | Glinka | CC BY-SA 3.0 |