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math.CO2025
Anisotropy and the -theorem for simplicial spheres
Eric Katz
We give an exposition of the proof of the lower bound part of the -theorem for simplicial spheres by Adiprasito, Papadakis, and Petrotou.
math.CO2025
Volume Polynomials and Log-concavity of the Characteristic Polynomials of Matroids
Eric Katz
The Rota--Heron--Welsh conjecture (now a theorem of Adiprasito, Huh, and the author) asserts the log-concavity of the characteristic polynomial of matroids. We give an exposition o…
math.CO2024
Matroidal Mixed Eulerian Numbers
Eric Katz, Max Kutler
We make a systematic study of matroidal mixed Eulerian numbers which are certain intersection numbers in the matroid Chow ring generalizing the mixed Eulerian numbers introduced by…