6 problems

Let $\operatorname{Par}_n$ denote the set of partitions with at most $n$ parts. A $(0,1)$-substitution map is an operator $\varphi$ on…

Bounded Littlewood identities. Both displayed identities hold.

The branching coefficient formula. The coefficients are

The partially asymmetric simple exclusion process is described using a deformed Markov matrix, with deformation parameter $\xi$ and system variables $\mathbf{x}$. For each positive…

Let $\lambda=(\lambda_1,\lambda_2,\dots,\lambda_m)$ be a partition, and let $K_{\lambda}(\xi)$ denote the Koornwinder moment defined by … where $Z_N$ is the ASEP partition function…

Let $m_0(\lambda)$ be the multiplicity of zero parts of the partition $\lambda$, let $P_\lambda(x_1,\dots,x_n;t)$ be the Hall–Littlewood polynomial, and let $b_\lambda(t)$ be its s…