Discrete CATS Seminar
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U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

FALL 2009

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"Ehrhart Polynomials, h*-vectors and triangulations of matroid polytopes"

David Haws

University of Kentucky

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Monday, October 19, 2009

4:00 pm, 845 Patterson Office Tower

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Abstract:

Matroids naturally encapsulate the combinatorial notion of
independence. They are found in matrices, graphs, transversals, point
configurations, hyperplane arrangements, greedy optimization, and
pseudosphere arrangements to name a few. One of the reasons matroids
have become fundamental objects in pure and applied combinatorics are
their many equivalent axiomatizations. In this talk I will define
matroids and matroid polytopes and present a new result that the
Ehrhart polynomial of matroid polytopes can be computed in polynomial
time when the rank is fixed. Second, I will discuss two conjectures
about the h*-vector and coefficients of Ehrhart polynomials of matroid
polytopes and provide theoretical and computational evidence for their
validity. Time permitting I will also present a variant of White's
conjecture which states that every matroid polytope has a regular
unimodular triangulation. I will show computational evidence
supporting this new conjecture and propose a combinatorial condition
on simplices sufficient for unimodularity.