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math.CO2026
A note on the ultra log-concavity of matroid intersection
Adam Schweitzer
In 1971, Mason conjectured that the numbers of independent sets of fixed size in a matroid constitute an ultra log-concave sequence. In 2020, this conjecture was proven by Brändén…
math.CO2026
Measurable Matroids: Foundations and Min--Max Theorems
Kristóf Bérczi, András Imolay, Ádám Schweitzer
We develop a measure-theoretic analogue of matroid theory on standard atomless measure spaces. Motivated by the quotient-convergence framework for submodular set functions, our aim…
math.CO2026
Existence of Kähler algebras with Chow polynomials as Hilbert series
Adam Schweitzer, Lorenzo Vecchi
In this article, we study Chow polynomials of weakly ranked posets and prove the existence of Gorenstein algebras with the Kähler package such that their Hilbert--Poincaré series a…