4 problems

For $n,k\in\mathbb{N}$, let $\Theta_{e_k}$, $\nabla$, and $\omega$ be the indicated symmetric-function operators, let $p_n$ and $p_{n,n(k+1)}$ be the relevant symmetric functions,…

For $m,n\in\mathbb{N}$, let $e_{m,n}$ be the rectangular symmetric function, let $\Theta_{e_k}$ be the theta operator indexed by $e_k$, and let $\mathsf{LRD}(m+k,n+k)^{\ast k}$ den…

Let $m,n\in\mathbb{N}$, let $d=\gcd(m,n)$, and let $p_{m,n}$ be the symmetric function associated with rectangular paths. For a rectangular path $\pi\in\mathsf{LRP}(m,n)$, let…

Let $m,n>0$, let $\mu=\mu_1\cdots\mu_k\vdash n$ be a composition as used in the paper, and define … Let $\mathrm{Q}_{m,n}$ be the rational shuffle operator, $1$ the unit symmetric…