Chow rings of matroids were instrumental in the resolution of the Heron–Rota–Welsh
Conjecture by Adiprasito, Huh, and Katz and in the resolution of the Top-Heavy Conjecture …

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 …

There has been much work on strong and weak Lefschetz conditions for graded Artinian
algebras A, especially those that are Artinian Gorenstein. A more general invariant of an …

The Jordan type of an element $\ell $ of the maximal ideal of an Artinian k-algebra A acting
on an A-module M of k-dimension n, is the partition of n given by the Jordan block …

Given a simple graph, consider the polynomial ring with coefficients in a field and variables
identified with the edges of the graph. Given a non-empty even cardinality Eulerian …

Let $ R $ be a standard graded Gorenstein algebra over a field presented by quadrics. In
[Compositio Math. 129 (2001), no. 1, 95–121], Conca-Rossi-Valla show that such a ring is …

We associate with every pure flag simplicial complex a standard graded Gorenstein-algebra
whose homological features are largely dictated by the combinatorics and topology of. As …

Abstract Conca–Rossi–Valla ask if every quadratic Gorenstein ring of regularity three is
Koszul. In, we use idealization to answer their question, proving that in nine or more …

Let R= 𝕂 [x 1,…, xn] and I⊂ R be a homogeneous ideal. We first obtain certain sufficient
conditions for the subadditivity condition of R/I. As a consequence, we prove that if I is …

The rate of a standard graded $ K $-algebra $ A $ is a measure of the growth of the shifts in
a minimal free resolution of $ K $ as an $ A $-module. In particular $ A $ has rate one if and …