2 problems

Unimodality conjecture. (i) If $X$ is a conjugacy class of involutions in $W(A_n)$ or $W(B_n)$, then the even/odd length profile of $X$ is unimodal. (ii) If $X$ is the set of invol…

Unimodality and log-concavity conjecture. The even and odd involution length profiles of $W(A_n)$ are log-concave, while the even and odd involution length profiles of $W(B_n)$ and…