The Topology of Restricted Partition Posets

GEOMETRY AND CELL COMPLEXES
Topic:The Topology of Restricted Partition Posets
Speaker:Richard Ehrenborg
Affiliation:University of Kentucky; Member, School of Mathematics
Date:Tuesday, November 2
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/gcell/ehrenborg

The d-divisible partition lattice is the collection of all partitions of an n-element set where each block size is divisible by d. Stanley showed that the Mobius function of the d-divisible partition lattice is given (up to a sign) by the number of permutations on n-1 elements where every dth position is a descent. Wachs showed that this lattice has an EL-shelling, and hence obtained as a corollary that the homotopy type of the order complex is a wedge of spheres. Finally, Calderbank, Hanlon and Robinson considered the action of the symmetric group on the top homology group and showed it is a Specht module of a border strip corresponding to the composition (d,...,d,d-1). Using a different proof approach, we will generalize these results to any descent pattern. This is joint work with JiYoon Jung.