Discrete CATS Seminar
####
**
**#####
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

##
"An Eulerian poset that lacks an R-labeling"

Richard Ehrenborg

University of Kentucky

###
Monday, October 5, 2009

4:00 pm, 845 Patterson Office Tower

####
Abstract:

The original notion of an R-labeling of a poset, due to Bjorner and
Stanley, uses a linearly ordered set for the labels. Bjorner and Wachs
extended this notion to when the label set has a partial order. We
take the next natural step and let the set of labels just have a
relation on it. We then reformulate the notion of R-labeling to triple
assignment. We obtain a structure theorem for triple assignments on
the butterfly poset. Using this we construct an Eulerian poset that
has a positive flag h-vector but does not have any R-labeling. We end
with many open questions.

This is joint work with Margaret Readdy.