Submit progress

on Tableaux problem 32

The statement

32.[Bjor] via [Bren2024a]*Prob. 1.9 Let $(W,S)$ be a Coxeter system and $u\leq v$ in $W$ . Is it true that then there are a Coxeter system $(W^{\prime},S^{\prime})$ and $w^{\prime}\in W^{\prime}$ such that

P_{u,v}(q)=P_{e^{\prime},w^{\prime}}(q)

where $e^{\prime}$ is the identity in $W^{\prime}$ ?

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.