We study semigroup algebras arising from lattice polytopes, compute their volume
polynomials (particularizing work of Hochster), and establish strong Lefschetz properties …

We study the anisotropy theorem for Stanley-Reisner rings of simplicial homology spheres in
characteristic 2 by Papadakis and Petrotou. This theorem implies the Hard Lefschetz …

June Huh found striking connections between algebraic geometry and combinatorics,
solved central problems in combinatorics that had remained open for decades, and …

Polynomials which afford nonnegative, real‐rooted symmetric decompositions have been
investigated recently in algebraic, enumerative and geometric combinatorics. Brändén and …

Let Δ be an (abstract) simplicial complex on n vertices. One can define the Artinian
monomial algebra A (Δ)= k [x 1,…, xn]/〈 x 1 2,…, xn 2, I Δ〉, where k is a field of characteristic …

The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by
their number of elements. The chain polynomials of the partition lattices and their standard …

Generalizing the strong Lefschetz property for an $\mathbb {N} $-graded algebra, we
introduce the multigraded strong Lefschetz property for an $\mathbb {N}^ m $-graded …

The theta polynomial of a triangulation $\Delta $ of a ball with boundary $\partial\Delta $ is
defined as the difference of the $ h $-polynomial of $\partial\Delta $ from the $ h …

In this work, we investigate the presence of the weak Lefschetz property (WLP) and Hilbert
functions for various types of random standard graded Artinian algebras. If an algebra has …

We calculate the determinant of the bilinear form in middle degree of the generic artinian
reduction of the Stanley-Reisner ring of an odd-dimensional simplicial sphere. This proves …