"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.