12 papers
Exchange Interactions and Magnon Spectra in bcc Fe(001) Thin Films: A Computational Study
Joanna Marciniak, Wojciech Marciniak, Jorge Luis Briseño-Gómez +1
We combined density functional theory with atomistic spin dynamics to understand how surfaces influence magnon dispersion. For this purpose, we investigate thin layers of body-cent…
Characterizing Steiner Systems via Betti Numbers of Monomial Ideals
Guillermo Alesandroni, Christopher Chin, Noah Ripke
Given a point set and a collection of -subsets of , we create a monomial ideal whose Betti numbers completely determine whether the pair is a Steiner sy…
Families of finite sets in which no set is covered by the union of the others
Guillermo Alesandroni
Let F be a finite nonempty family of finite nonempty sets. We prove the following: (i) F satisfies the condition of the title if and only if for every pair of distinct subfamilies…
The Erdos-Faber-Lovasz conjecture for weakly dense hypergraphs
Guillermo Alesandroni
Generalizing the concept of dense hypergraph, we say that a hypergraph is weakly dense, if no k in the half-open interval [2,sqrt(n)) is the degree of more than k^2 vertices. In ou…
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…
Structural decomposition of monomial resolutions
Guillermo Alesandroni
We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decompo- sition has multiple…
Minimal Resolutions of Dominant and Semidominant Ideals
Guillermo Alesandroni
We construct the minimal resolutions of three classes of monomial ideals: dominant, 1-semidominant, and 2-semidominant ideals. The families of dominant and 1-semidominant ideals ex…