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math.AC2019
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…
math.AC2019
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…
math.AC2019
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…