Slop Factor

Matroid flat counts are not unimodal

Alexander Divoux, Chayim Lowen, Shouda Wang

arXiv:2607.22515v1 Primary: math.CO

Abstract

We give counterexamples to Rota's 1970 conjecture that the sequence counting flats of varying rank in a matroid is unimodal. More specifically, inspired by Larson's recent disproof of the stronger log-concavity conjecture of Mason, we explain a mechanism which turns failures of log-concavity for flats into failures of unimodality under suitable conditions.

Disclosure

“MODAL 7 How the counterexamples were found. The starting point of this paper was an attempt to study the convexity of (Wi−1 )i , which is weaker than log-concavity but stronger than unimodality. We used ChatGPT 5.6 Pro to search for a counterex- ample to this weaker property. Based on a suggestion of the authors, ChatGPT 5.6 Pro returned a non-convex example built using a q-lift. We quickly realized this construction could in fact be adapted and”

PDF page 7
Classification
Substantial mathematical content or result generation
Multiplier
10
Verified

Structural counts

Pages 8 pdf
Theorems 1 pdf fallback
Lemmas 2 pdf fallback
Propositions 0 pdf fallback
Corollaries 0 pdf fallback
Definitions 0 pdf fallback
Displayed equations 32 pdf fallback
Bibliography entries 1 pdf fallback
Appendix pages 0 estimated

Count notes

  • arXiv source was unavailable; PDF-text fallbacks were used.
  • Appendix pages include the first PDF page with an explicit Appendix heading through the final page.