5 problems

Let $c1_{2,3}(s,n)$ denote the quantity counting the relevant continuous multiline-queue configurations, let $N$ be the total size parameter used in the paper, and let $f_{(s,s)}$…

Let $b3^\ell(s,n)$ denote the number of continuous multiline queues with the specified one-wrapping configuration, and let $f_{(n-1,s+1)}$ denote the relevant hook-length count. Th…

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…