Matroid flat counts are not unimodal

2026/07/24 by Alexander Divoux, Chayim Lowen, Shouda Wang · 1 voice
#math.CO

paper · pdf

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.

Discussions

• Matroid theory is currently experiencing a wave of counterexamples to several influential conjectures through the use of AI. Notably, in late June 2026, Matt Larson disproved log-concavity for the Whi [stackexchange, 15 points]

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