5 problems

Let {\text{\boldmath p}}=(p_1,\ldots,p_m) and {\text{\boldmath q}}=(q_1,\ldots,q_m) be as above, let \lambda={\text{\boldmath p}}\times{\text{\boldmath q}}, let $\mu$…

Let shifted Jack Littlewood–Richardson coefficients be defined for partitions with $|\lambda|\leq|\mu|+|\nu|$. Shifted Jack congruence conjecture. The adjacent-triple congruence co…

Let $\mathscr{P}$ denote the set of partitions, let $E_k(\,\cdot\,;\epsilon,0)$ be the quantum KdV expression defined in the paper, and let $Q_j$ and $\ell(\nu)$ denote the shifted…

Let $\Lambda^*=\mathbb{Q}[Q_2,Q_3,\dots]$ be the algebra of shifted symmetric functions on partitions, and let $E_k^{[m]}(\lambda;c)$ be the expressions defined in the paper. Zagie…

Alexandersson–Féray's conjecture. For shifted Jack functions, these structure coefficients are Laurent polynomials in $\alpha$ with non-negative integer coefficients. The supplied…