4 problems

Bounded-complexity rapid-mixing conjecture. The Markov chain $\mathcal{MC}_{\sf SVT}(\lambda,N,S)$ is rapidly mixing for every $(\lambda,N,S)\in\mathcal{F}_d$.

Lusztig-involution conjecture. For every partition $\lambda$,

Let $w$ be a permutation and $\lambda$ a partition, and let $\operatorname{SLT}_{w\lambda}$ be the set of semistandard set-valued skyline tableaux of shape $w\lambda$. Define the La…

Assume $x\equiv a\pmod{k-1}$, where $2\leq a\leq k-1$. Let … and let $\operatorname{PC}_x^k(n,m)$ denote the relevant prographs and $\operatorname{\mathbb{S}}(\lambda/\mu,\rho)$ th…