7 papers · 1 filter
Monomial invariants applied to graph coloring
Guillermo Alesandroni
This article is built upon three main ideas. First, for a class of monomial ideals, it is proven that the multiplicity of an ideal equals the number of realizations of its codimens…
Betti numbers of monomial ideals in four variables
Guillermo Alesandroni
We express the multigraded Betti numbers of monomial ideals in 4 variables in terms of the multigraded Betti numbers of 66 squarefree monomial ideals, also in 4 variables. We use t…
Monomial multiplicities in explicit form
Guillermo Alesandroni
In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1…
The order of dominance of a monomial ideal
Guillermo Alesandroni
Let S be a polynomial ring in n variables over a field, and let M be a monomial ideal of S. We introduce a new invariant, called the order of dominance of S/M, denoted odom(S/M), w…
Hilbert's Syzygy Theorem for monomial ideals
Guillermo Alesandroni
We give a new proof of Hilbert's Syzygy Theorem for monomial ideals. In addition, we prove the following. If S=k[x_1,...,x_n] is a polynomial ring over a field, M is a squarefree m…
Monomial ideals with large projective dimension
Guillermo Alesandroni
Let S be a polynomial ring in n variables, over an arbitrary field. We give the total, graded, and multigraded Betti numbers of S/M, for every monomial ideal M in S. We also give a…