3 problems

Let $W_{\mathcal{T}}$ be the double-affine Weyl monoid, let $\widetilde{\Delta}^+$ denote the positive double-affine real roots, and let $\ell$ be the length function. Deodhar's in…

The transverse-slice counting conjecture. There exists a polynomial $R_{x,y}\in\mathbb{Z}[v]$, independent of $k$, of degree $\ell(y)-\ell(x)$ such that

Let $W_{\mathcal{T}}$ be the double-affine Weyl monoid, equipped with its Bruhat order $<$ and length function $\ell$. Write $x\lhd y$ when $y$ covers $x$, meaning that $x<y$ and t…