University of Kentucky Discrete CATS and WILDCATS Seminars
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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!

and

UK
WILDCATS
Seminar

845 PATTERSON OFFICE TOWER

2011 -- 2012

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"Euler flag enumeration of Whitney stratified spaces"

Margaret Readdy

University of Kentucky

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Monday, October 24, 2011

4:00 pm

845 POT

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Abstract:

The flag vector contains all the face incidence data of a polytope,
and in the poset setting, the chain enumerative data. It is a
classical result due to Bayer and Klapper that for face lattices of
polytopes, and more generally, Eulerian graded posets, the flag vector
can be written as a cd-index, a non-commutative polynomial which
removes the generalized Dehn-Sommerville relations, that is, all the
linear redundancies among the flag vector entries discovered by Bayer
and Billera. This result holds for regular CW complexes.

We relax the regularity condition to show the cd-index exists for
non-regular CW complexes by extending the notion of a graded poset to
that of a quasi-graded poset. This is a poset endowed with an
order-preserving rank function and a weighted zeta function. This
allows us to generalize the classical notion of Eulerian, and obtain a
cd-index in the quasi-graded poset arena.

Generally speaking, for an arbitrary quasi-graded poset the weighted
zeta function is not unique. However, for a manifold having a Whitney
stratification, selecting the weighted zeta function of an interval
using the Euler characteristic gives the extended notion of
Eulerianess geometric meaning.

This is joint work with Richard Ehrenborg and Mark Goresky.

Coming Attractions
Seminar Archive

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We would like to thank
Benjamin Braun (NSF DMS-0758321),
Richard Ehrenborg (NSF DMS-0902063)
and
Margaret Readdy (Simons Foundation Collaboration Grant 2011--2016)
who continue to generously
support our speakers
with their grants.

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If you wish to be added to the seminar list, please
e-mail Margaret Readdy at readdy (at) ms.uky.edu