The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

Motivated by notions from coding theory, we study the generalized minimum distance (GMD)
function δ I (d, r) of a graded ideal I in a polynomial ring over an arbitrary field using …

We introduce and study the minimum distance function of a graded ideal in a polynomial
ring with coefficients in a field, and show that it generalizes the minimum distance of …

Using commutative algebra methods, we study the generalized minimum distance function
(gmd function) and the corresponding generalized footprint function of a graded ideal in a …

The aim of this work is to give degree formulas for the generalized Hamming weights of
evaluation codes and to show lower bounds for these weights. In particular, we give degree …

Arithmetical structures on a graph were introduced by Lorenzini in [9] as some intersection
matrices that arise in the study of degenerating curves in algebraic geometry. In this article …

Let $ S $ be a polynomial ring over a field $ K $, with a monomial order $\prec $, and let $ I $
be an unmixed graded ideal of $ S $. In this paper we study two functions associated to $ I …

In this paper, to any subset A⊂ Z n we explicitly associate a unique monomial projection Y
n, d A of a Veronese variety, whose Hilbert function coincides with the cardinality of the t-fold …

We study the regularity and the algebraic properties of certain lattice ideals. We establish a
map I ↦ ̃ I between the family of graded lattice ideals in an ℕ-graded polynomial ring over a …

We study various binomial and monomial ideals arising in the theory of divisors,
orientations, and matroids on graphs. We use ideas from potential theory on graphs and …