Patrik Noren
Powers of edge ideals.
Tue, 11/29/2011 - 15:01 — SomNambulAuthors: Oana Olteanu, Patrik Noren, Carmela Ferro, Mariella Murgia
Subjects: Commutative Algebra
AbstractWe compute the Betti numbers for all the powers of initial and final
lexsegment edge ideals. For the powers of the edge ideal of an anti-$d-$path,
we prove that they have linear quotients and we characterize the normally
torsion-free ideals. We determine a class of non-squarefree ideals, arising
from some particular graphs, which are normally torsion-free.Polytopes from Subgraph Statistics.
Wed, 11/17/2010 - 16:01 — SomNambulAuthors: Alexander Engstrom, Patrik Noren
Subjects: Combinatorics
AbstractWe study polytopes that are convex hulls of vectors of subgraph densities.
Many graph theoretical questions can be expressed in terms of these polytopes,
and statisticians use them to understand exponential random graph models.Relations among their Ehrhart polynomials are described, their duals are
applied to certify that polynomials are non-negative, and we find some of their
faces.- Read more
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Ideals of Graph Homomorphisms.
Fri, 02/26/2010 - 16:01 — SomNambulAuthors: Alexander Engstrom, Patrik Noren
Subjects: Commutative Algebra
AbstractIn this paper we introduce the ideals of graph homomorphisms.
They are natural generalizations of toric ideals from algebraic statistics
studied by Diaconis, Sturmfels, and Sullivant. They are toric ideals; and their
polytopes, for example the stable set polytope, are important in optimization
theory. They capture more information about graphs than just the graphs, since
we work with the category of graph homomorphisms.
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