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seminars:comb:abstract.200305wau

# The Order Dimension of Bruhat Order

## Abstract for the Combinatorics and Number Theory Seminar 2003 May 6

I consider the order dimension of infinite Coxeter groups under strong Bruhat order. In particular, I show that the order dimension of the affine Coxeter group An is at least n(n+1). To accomplish this, I exhibit an antichain of certain special elements called dissectors. I describe these dissectors in terms of rectangles within a specified array of generators in order to establish that we have an antichain and count its elements. I then use the fact that the order dimension dim(P) of a finitary poset P is at least the width of the subposet dis(P) of its dissectors.