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math.GR1998
A Generalization of an Alternating Sum Formula for Finite Coxeter Groups
Jason Fulman
For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Carter…
math.GR1998
Semisimple orbits of Lie algebras and card shuffling measures on Coxeter groups
Jason Fulman
Solomon's descent algebra is used to define a family of signed measures M(W,x) for a finite Coxeter group W and non-zero x. The measures corresponding to W of types A and B are kno…
math.CO1998
Descent algebras, hyperplane arrangements, and shuffling cards
Jason Fulman
Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon's descent algebra and another using random walk on chambers of hyperplane arrangements. These…