Speaker: Lou Billera, Cornell University
Enumeration in polytopes and Coxeter groups
There are curious parallels between the enumeration of faces and
flags in convex polytopes and the enumeration of chains in a standard partial
order - the Bruhat order - on the elements of an arbitrary Coxeter group.
Both define so-called Eulerian posets, but this is far from giving the
whole story. There are important invariants in each theory, the g-polynomial
for polytopes and the Kazhdan-Lusztig polynomial for Bruhat intervals,
that are known to have many similar properties. I will outline these
theories and their parallels, and offer some speculation on what may be
behind the similarities.
I will assume familiarity with neither polytopes nor Coxeter groups.
Department of Mathematical Sciences
George Mason University
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