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

2011 - 2012

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"Euler-Mahonian statistics via polyhedral geometry"

Ben Braun

University of Kentucky

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Monday, September 12, 2011

4:00 pm

845 POT

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Abstract:

A variety of descent and major index statistics have been defined for
symmetric groups, hyperoctahedral groups, and their generalizations.
Typically associated to pairs of such statistics is an Euler-Mahonian
distribution, a bivariate generating function identity encoding these
statistics. We use techniques from polyhedral geometry to establish
new multivariate generalizations for many of the known Euler-Mahonian
distributions. The original bivariate distributions are then
straightforward specializations of these multivariate identities. A
consequence of these new techniques are bijective proofs of the
equivalence of the bivariate distributions for various pairs of
statistics. This is joint work with Matthias Beck of San Francisco
State University.