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Joint Meeting of AMS, DMV, and ÖMG
June 16-19, 2005
Johannes Gutenberg University
Mainz, Germany

Organizers
Volker Bach, Mainz; Klaus D. Bierstedt, DMV; Susan Friedlander, Associate Secretary, AMS

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Posets from Total Positivity
by
Lauren Williams
MIT/ U.C. Berkeley

We discuss a family of posets that arise from Lusztig's theory of total positivity. These posets describe the cell decomposition of the totally nonnegative part of a flag variety, and are intimately related to the Bruhat order. We give enumeration and shellability results, focusing in particular on the Grassmannian and the complete flag variety. One corollary is a new q-analogue of the Eulerian numbers, which specializes to the Naryana numbers, Eulerian numbers, and binomial coefficients.

Date received: March 25, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caql-67.