Stability, fragility, and Rota's Conjecture

Details Stability, fragility, and Rota's Conjecture Stability, fragility, and Rota's Conjecture

2010-06-08

arxiv.org/abs/1006.1418v2

Mathematics

Combinatorics

32 pages

Scientific paper

Fix a matroid N. A matroid M is N-fragile if, for each element e of M, at least one of M\e and M/e has no N-minor. The Bounded Canopy Conjecture is that all GF(q)-representable matroids M that have an N-minor and are N-fragile have branch width bounded by a constant depending only on q and N. A matroid N stabilizes a class of matroids over a field F if, for every matroid M in the class with an N-minor, every F-representation of N extends to at most one F-representation of M. We prove that, if Rota's conjecture is false for GF(q), then either the Bounded Canopy Conjecture is false for GF(q) or there is an infinite chain of GF(q)-representable matroids, each not stabilized by the previous, each of which can be extended to an excluded minor. Our result implies the previously known result that Rota's conjecture holds for GF(4), and that the classes of near-regular and sixth-roots-of-unity have a finite number of excluded minors. However, the bound that we obtain on the size of such excluded minors is considerably larger than that obtained in previous proofs. For GF(5) we show that Rota's Conjecture reduces to the Bounded Canopy Conjecture.

Affiliated with

Also associated with

No associations

Rating

Stability, fragility, and Rota's Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability, fragility, and Rota's Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability, fragility, and Rota's Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-29370