A permutation of a set of objects is simply a rearrangement of those objects. If we have n of objects, then a permutation can be represented as a function from 1,2,...,n to 1,2,...,n. We say that a permutation w has property T if there exists i such that either w(i) is greater than w(i + 1), w(i + 2) or w(i + 2) is less than w(i), w(i + 1). A permutation w is T-avoiding if neither w nor its inverse have property T. We will present a classification of the T-avoiding permutations in the symmetric group, which is a Coxeter group of type A. In addition, we will discuss generalizations to other Coxeter groups and classify the T-avoiding elements in Coxeter groups of types B, which can be thought of as the group that rearranges coins and flips them over.
This poster was presented by my undergraduate research students Joseph Cormier, Zachariah Goldenberg, and Jessica Kelly (Plymouth State University) on January 6, 2012 at the 2012 Joint Mathematics Meetings in Boston, MA.