Timeline for Matroids relaxations of a given matroid
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2014 at 8:05 | comment | added | Gordon Royle | You were unlucky in that for all three of those matroids, the set of circuit-hyperplanes happens to coincide with the set of nonbases. As for the first question, I don't know of any natural (non-matroidal) place where all relaxations of a given matroid are considered, though there are technical results about such things. | |
| Dec 12, 2014 at 10:19 | history | bounty ended | Camilo Sarmiento | ||
| Dec 12, 2014 at 10:18 | vote | accept | Camilo Sarmiento | ||
| Dec 12, 2014 at 10:17 | comment | added | Camilo Sarmiento | I'll take your answer, but let me first reiterate my first question: do you know if the relaxations (aka weak preimages) of a matroid naturally show up in some context? (with apologies if that's mentioned in Matroid Theory's 2nd edition, since currently I have no access to it). | |
| Dec 12, 2014 at 10:13 | comment | added | Camilo Sarmiento | Incidentally, it is somehow odd to me that for all of the matroids I tried (Fano, Vamos, K_4, Pappus, NonPappus), all the "naive relaxations" adding some nonbases were actually matroids (I got the same outcome as you when I tried the matroid J). Is there any general reason why this is the case other than coincidence, or "Fano, Vamos, Pappus, K_4 have few nonbases"? | |
| Dec 12, 2014 at 10:07 | comment | added | Camilo Sarmiento | Thank you for the comprehensive answer. The code I used was essentially the same as yours, only that instead of ranging over nonbases, I was ranging over subsets thereof (also, sloppily, I was doing my manipulations with lists of sets instead of the native lists of frozensets for the matroids class). | |
| Dec 12, 2014 at 5:00 | history | answered | Gordon Royle | CC BY-SA 3.0 |