Speaker:
Samuel Hsiao, University of Michigan
Title:
Orienting distributive lattices
Abstract:
Given a finite poset P, there is an associated distributive
lattice J(P) (the "Birkhoff transform")
consisting of the order ideals of P ordered by inclusion.
In this talk I will introduce a signed analog of
the Birkhoff transform; the notion of an order ideal will
be replaced by
that of a "signed filter." The resulting poset, B(P),
of signed filters turns out to be Eulerian and ELshellable; hence by
a theorem of Bjorner it is the face poset of a regular
CW sphere. There is a combinatorial method for
computing its cdindex that has a counterpart
in the flag enumerative theory of oriented matroids.
In fact, B(P) seems to have the general feel of an oriented
matroid, with J(P) playing the role of the geometric lattice of flats.
I will also mention a close connection between
chainenumeration in B(P) and
Stembridge's enriched version of the NeggersStanley conjecture.
