Let $ R $ be a polynomial ring over an algebraically closed field and let $ A $ be a standard
graded Cohen-Macaulay quotient of $ R $. The authors state that $ A $ is a level algebra if …

Our work, which makes an extensive use of both algebraic and combinatorial techniques, in
particular includes:(i) A characterization of the first half of a pure O-sequence, which yields …

We classify all possible $ h $-vectors of graded artinian Gorenstein algebras in socle degree
4 and codimension $\leq 17$, and in socle degree 5 and codimension $\leq 25$. We obtain …

Let R= k [x1,…, xr] denote the polynomial ring in r variables over a field k, with maximal ideal
M=(x1,…, xr), and let V⊂ Rj denote a vector subspace of the space Rj of degree-j …

In this paper we prove the existence of minimal level artinian graded algebras having socle
degree r and type t and describe their h-vector in terms of the r-binomial expansion of t. We …

In this paper we consider Artin compressed local algebras, that is, local algebras with
maximal length in the class of those with given embedding dimension and socle type. They …

Log-concave Gorenstein sequences Page 1 J CA JOURNAL OF COMMUTATIVE ALGEBRA
Volume 16 (2024), No. 1, 25–36 DOI: 10.1216/jca.2024.16.25 © Rocky Mountain Mathematics …

$(1, 3, 6, 10, 15, 21, 28, 27, 27, 28) $ is a level $ h $-vector! This example answers
negatively the open question as to whether all codimension 3 level $ h $-vectors are …

Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers
of the variables, and finitely generated submodules of the ring's graded dual, is generalized …

The authors construct the global Macaulay inverse system LZ for a zero-dimensional
subscheme Z of projective n-space Pn over an algebraically closed field k, from the local …