Discrete CATS Seminar
UNIVERSITY OF KENTUCKY
DISCRETE CATS SEMINAR
DISCRETE MATH AND COMBINATORICS: ALGEBRAIC & TOPOLOGICAL SEMINAR
113 PATTERSON OFFICE TOWER
"A Recursive Structure on Bruhat Intervals"
University of Kentucky
Monday, December 3, 2007
4:00 pm, 113 Patterson Office Tower
Given a group whose generators are involutions (such as a symmetric
group) we can define a partial order on the group elements by defining
one element to be less than another if, when both are written as
reduced words on the generators, the one is a subword of the other.
This is called the Bruhat order.
In a paper based largely on his doctoral thesis, Nathan Reading gives
a structural recursion on intervals in Bruhat order. This structural
recursion gives a new proof that (the order complex of) open Bruhat
intervals are always PL Spheres and also leads to a recursive formula
for the cd-indices of Bruhat intervals.
I will outline some requisite background concepts, then present the
recursion, given in terms of the operations of forming a pyramid,
shaving, and zipping, and gives some consequences of this structure,
including a recursion on the cd-indices.