It concerns matroid flats, not the different conjecture
about counts of independent sets.
Larson (2026) gave a counterexample consisting of the graphic matroid of four internally disjoint paths between two
vertices, of lengths 1, 26, 26, and 26. Its matroid
rank is 76, and
The article credits GPT-5.5 Pro with finding a precursor and supplies a proof not requiring a computer.
Larson, M. "Counterexamples to Two Conjectures about Matroids." 2 Jul 2026. https://arxiv.org/abs/2607.02208.Mason,
J. H. "Matroids: Unimodal Conjectures and Motzkin's Theorem." In Combinatorics:
Proceedings of the Conference on Combinatorial Mathematics, Mathematical Institute,
Oxford, 1972 (Ed. D. J. A. Welsh and D. R. Woodall). Southend-on-Sea,
England: Institute of Mathematics and its Applications, pp. 207-220, 1972.
of matroid flats of matroid
rank 
form a logarithmically concave sequence,
so
