6 papers
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…
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…
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…
Clique number of xor-powers of Kneser graphs
Zoltán Füredi, András Imolay, Ádám Schweitzer
Let denote the clique number of the xor-product of isomorphic Kneser graphs KG(n,k). Alon and Lubetzky investigated the case of complete graphs as a coding th…
Clique number of Xor products of Kneser graphs
András Imolay, Anett Kocsis, Ádám Schweitzer
In this article we investigate a problem in graph theory, which has an equivalent reformulation in extremal set theory similar to the problems researched in "A general 2-part Erdős…
Capacity of Lorentzian polynomials and distance to binomial distributions
Ádám Schweitzer
In this paper we study the capacity of Lorentzian polynomials. We give a new proof of a theorem of Brändén, Leake and Pak. Our approach is probabilistic in nature and uses a lemma…