Log-Concavity of Flats of Matroids
Refuting log-concavity of the flat counts is weaker than refuting their unimodality, since log-concavity is the stronger property. A counterexample to unimodality followed three weeks later and is tracked separately as Rota's Unimodality Conjecture for Matroid Flats; this paper came first.
Exact FrontierDelta
Scope and record
Occurred: Jul 2, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Editorial metadata: CC BY 4.0; linked content retains its own rights.
Canonical aliases: Log-Concavity of Flats of Matroids · Mason flat log-concavity
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Matt Larson
human · human collaborator
ChatGPT-5.5 Pro
model · ai model contributor · OpenAI
Claude Opus 4.8
model · ai model contributor · Anthropic
Lineage and corrections
This event attributed to Matt Larson
This event attributed to ChatGPT-5.5 Pro
This event attributed to Claude Opus 4.8
White's Conjecture on Matroids evidence for this event
VibeMathed record: Log-Concavity of Flats of Matroids evidence for this event
Refuting log-concavity of the flat counts is weaker than refuting their unimodality, since log-concavity is the stronger property. A counterexample to unimodality followed three weeks later and is tracked separately as Rota's Unimodality Conjecture for Matroid Flats; this paper came first. parent of this event
GPT-5.5 Chat Log evidence for this event
Log-Concavity of Flats of Matroids parent of this event
Act on this frontier