5 problems

Let $n$ be a positive integer, let $\lambda=(\lambda_1\geq\cdots\geq\lambda_n\geq 0)$ be a partition, and consider the multispecies totally asymmetric simple exclusion process (TAS…

Grouping conjecture. There is a way to group permuted basement tableaux so that the weight in each group equals the weight of one MLQ.

Let $N\ge n$, let $\mathbf{k}=(k_1\ge\cdots\ge k_r\ge 1)$ be a partition, and let $\mathbf{k}'$ be its conjugate. For $S\subseteq [r]$, let $\mathbf{k}(S)$ be the partition consist…

Let $N\ge n>k\ge 1$ and let $0\le b_1<\dots<b_n\le N-1$. For the permutation $s_kw_0$ obtained by applying the simple reflection $s_k$ to the longest permutation $w_0$, let $A_k$ b…

Let $\mathcal Q$ be a multiline queue with state space $\Omega^{FM}_m$, and let $\Omega_m$ be the state space of the corresponding inhomogeneous multispecies exclusion process. For…