Work

Neither simpliciality nor mutation connectivity: conjectures of Las Vergnas and Cordovil-Las Vergnas fail

Year: 2026

Type: preprint

Abstract: We construct a simple rank-$7$ oriented matroid on $24$ elements with no simplicial tope, disproving the Las Vergnas simplex conjecture from 1980. We then show that the mutation graph on uniform oriented matroids is disconnected for infinitely many values of rank $r$ and ground-set size $n$, disproving the Cordovil--Las Vergnas conjecture from 1988.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.15850

Authors: Gu, Qiyuan, Knauer, Kolja

Institutions: University of Chicago, Centre de Recerca Matemàtica, Universitat de Barcelona

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Regional Development Fund, Agencia Estatal de Investigación

Awards: G1175115578, G14461421, G2262748287, G294895050, G300979063, G3480869486, G410571670, G425668148, G451917667, G5080475149, G523076202, G5539308778, G5967599077, G6033112984, G6307970414, G7084143925, G84477964

OpenAlex ID: W7213253456

Cites:

Cited by: 2

Related to: 10