Timeline for Convex hull of total orders
Current License: CC BY-SA 3.0
14 events
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| Aug 12, 2014 at 2:50 | comment | added | Lev Borisov | I have a feeling that the number of facets of the total order polytope grows faster than a polynomial in $n$. As a result, the polytope can not be described by relations with a bounded set of indices. | |
| S Aug 11, 2014 at 19:52 | history | suggested | Mostafa - Free Palestine | CC BY-SA 3.0 |
correcting a typo
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| Aug 11, 2014 at 19:17 | review | Suggested edits | |||
| S Aug 11, 2014 at 19:52 | |||||
| Aug 11, 2014 at 18:55 | vote | accept | Mostafa - Free Palestine | ||
| Aug 11, 2014 at 18:54 | vote | accept | Mostafa - Free Palestine | ||
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| Aug 11, 2014 at 18:49 | history | bounty ended | Per Alexandersson | ||
| Aug 11, 2014 at 18:41 | comment | added | Per Alexandersson | @EmilJeřábek: Good question! I feel this is related to the Birkhoff polytope, and also the convex hull of all Alternating Sign matrices of a fixed size. There is an article by J. Striker, giving the inequalities/equalities for the latter case, it is not a trivial task. So it might be that the inequalities for partial orders can be tricky to find. Perhaps some actual experimentation in Sage is in order... | |
| Aug 11, 2014 at 18:36 | comment | added | Emil Jeřábek | Nice! The inequalities are valid for any partial order if we put $w_{ij}=0$ when $i,j$ are incomparable, and your example shows that some partial orders are not in the convex hull of total orders. A natural follow-up question is then whether the inequalities describe the convex hull of partial orders. | |
| Aug 11, 2014 at 18:35 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Aug 11, 2014 at 18:22 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Aug 11, 2014 at 18:08 | history | undeleted | David E Speyer | ||
| Aug 11, 2014 at 18:08 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Aug 11, 2014 at 16:31 | history | deleted | David E Speyer | via Vote | |
| Aug 11, 2014 at 16:30 | history | answered | David E Speyer | CC BY-SA 3.0 |