Volkmar Welker
Spectra of Symmetrized Shuffling Operators.
Tue, 02/15/2011 - 16:01 — SomNambulAuthors: Franco Saliola, Volkmar Welker, Victor Reiner
Subjects: Combinatorics
Abstract(Abridged abstract) For a finite real reflection group W and a W-orbit O of
flats in its reflection arrangement---or equivalently a conjugacy class of its
parabolic subgroups---we introduce a statistic on elements of W. We then study
the operator of right-multiplication within the group algebra of W by the
element whose coefficients are given by this statistic.Commutative Algebra of Statistical Ranking.
Tue, 01/11/2011 - 16:01 — SomNambulAuthors: Bernd Sturmfels, Volkmar Welker
Subjects: Commutative Algebra
AbstractA model for statistical ranking is a family of probability distributions
whose states are orderings of a fixed finite set of items. We represent the
orderings as maximal chains in a graded poset. The most widely used ranking
models are parameterized by rational function in the model parameters, so they
define algebraic varieties. We study these varieties from the perspective of
combinatorial commutative algebra. One of our models, the Plackett-Luce model,
is non-toric.The Betti polynomials of powers of an ideal.
Tue, 10/20/2009 - 12:53 — SomNambulAuthors: Volkmar Welker, Juergen Herzog
Subjects: Commutative Algebra
AbstractFor an ideal $I$ in a regular local ring or a graded ideal $I$ in the
polynomial ring we study the limiting behavior of the Betti numbers of S/I^k as
k goes to infinity. By Kodiyalam's result it is known that in each homological
degree the Betti number is a polynomial for large k. We call these polynomials
the Kodiyalam polynomials and encode the limiting behavior in their generating
polynomial. It is shown that the limiting behavior depends only on the
coefficients on the Kodiyalam polynomials in the highest possible degree.Buchsbaum* complexes.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Christos A. Athanasiadis, Volkmar Welker
Subjects: Combinatorics
AbstractWe introduce a class of simplicial complexes which we call Buchsbaum* over a
field. Buchsbaum* complexes generalize triangulations of orientable homology
manifolds. By definition, the Buchsbaum* property depends only on the geometric
realization and the field. Characterizations in terms of simplicial and local
cohomology are given. It is shown that Buchsbaum* complexes are doubly
Buchsbaum. Applications to enumerative and graph theoretic properties of
Buchsbaum* complexes are provided. The former lead to a conjecture which
extends a version of the g-conjecture by Bjoerner and Swartz.
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