Descent Algebras, Hyperplane Arrangements, and Shuuing Cards

This note establishes a connection between Solomon's descent algebras and the theory of hyperplane arrangements. It is shown that card-shu ing measures on Coxeter groups, originally de ned in terms of descent algebras, have an elegant combinatorial description in terms of randomwalk on the chambers of hyperplane arrangements. As a corollary, a positivity conjecture of Fulman is proved. 2