Coxeter groups can be thought of as generalized reflections groups. In particular, a Coxeter group is generated by a set of elements of order two. Every element of a Coxeter group can be written as an expression in the generators, and if the number of generators in an expression is minimal, we say that the expression is reduced. We say that an element w of a Coxeter group is T- avoiding if w does not have a reduced expression beginning or ending with a pair of non-commuting generators. In this talk, we will classify the T-avoiding elements of type F_5. We conjecture that our classification holds more generally for F_n with n ≥ 5.
This talk was given by my undergraduate research students Ryan Cross, Katie Hills-Kimball, and Christie Quaranta (Plymouth State University) on April 21, 2012 at the 2012 Hudson River Undergraduate Mathematics Conference at Western New England University.