Tuesday, November 30
Patricia Hersh, North Carolina State University and Cornell University
Given any finite Coxeter group and any minimal set S of generators, Eric Babson and Vic Reiner introduced an associated ``Coxeter-like complex'' whose cells are cosets of ``parabolic subgroups'', i.e. subgroups generated by a subset of S. They conjectured a lower bound on the connectivity in the case where W is the symmetric group and S is a set of transpositions. I will discuss the proof of this conjecture and how this relates to the question of which trees admit pleasant notions of inversions and weak order on the set of labelings of the tree.
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