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.
Although the whole sequence need not be logarithmically concave, the first three nontrivial Whitney numbers satisfy a stronger inequality.
Dong and Liu (2026) proved for every loopless matroid
of matroid rank at least three. This points-lines-planes
result does not restore the refuted assertion for all ranks.
Dong, Y. and Liu, Y. "A Weighted Inequality for Matroid Flats and Log-Concavity of Whitney Numbers." 21 Oct 2026. https://arxiv.org/abs/2610.29893.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
for every loopless matroid
of matroid rank at least three. This points-lines-planes
result does not restore the refuted assertion for all ranks.
