The University of Michigan Combinatorics Seminar


Abstract 

Given a finite poset P, there is an associated distributive lattice J(P) consisting of the order ideals of P ordered by inclusion. In this talk I will consider a signed analogue of this association, where the notion of an order ideal is replaced by that of a ``signed order ideal.'' The resulting poset of signed order ideals is Eulerian and ELshellable. Its cdindex, which encodes basic chainenumerative information, can be computed by summing entries of the flag hvector of J(P). The proof of the latter result is based on earlier work of Billera, Ehrenborg, and Readdy establishing a similar relationship between the cdindex of an oriented matroid and the flag hvector of the underlying matroid. 