Some Hecke Algebra Products and Corresponding Random Walks

Rosena R. X. Du, Richard P. Stanley

Let $\mathbf{i}=1+q+...+q^{i-1}$. For certain sequences $(r_1,...,r_l)$ of positive integers, we show that in the Hecke algebra ${\mathcal{H}}_n(q)$ of the symmetric group $\mathfrak{S}_…