4 problems

Let $W$ be a finite Coxeter group with simple generators $S$. For $I,J\subset S$, let $X_{IJ}$ be the set of distinguished representatives used in the double-coset decomposition, a…

Let $n$ be a positive integer, let $\lambda,\mu\vdash n$, and let $q$ be a prime power. Write $\operatorname{GL}_n(\mathbb F_q)$ for the general linear group and…

Higher-order asymptotic conjecture. There exists a constant $c>0$ such that

Let $S_n$ be the symmetric group, and let $p_n$ denote the total number of distinct parabolic double cosets in $S_n$, equivalently … where $c_w$ is the number of parabolic double c…