Existence of Strong Lefschetz algebras with Chow polynomials as Hilbert series

Abstract: In this article, we study Chow polynomials of weakly ranked posets and prove the existence of Gorenstein algebras with the strong Lefschetz property such that their Hilbert-Poincaré series agrees with the Chow polynomial, providing evidence in support of a conjecture by Ferroni, Matherne and the second author. This allows us to show strong inequalities for the coefficients of Chow polynomials; we prove log-concavity for all posets of weak rank at most six and provide counterexamples to log-concavity for any higher rank. For ranked posets we recover an even stronger condition, showing that the differences between consecutive coefficients constitute a pure O-sequence.