7 problems

Let a labelled parallelogram polyomino of size $m\times n$ be a pair of northeast lattice paths on an $m\times n$ grid, with labels on the cells adjacent to the prescribed boundary…

Let $\mathcal{R}^{(2,2)}$ be the space of $S_n$-coinvariants for two sets of commuting variables and two sets of anticommuting variables, and let $\mathcal{F}$ denote its Frobenius…

Let $alpha$ be a composition, let $mathsf{RTT}0(alpha)$ be the set of $alpha$-trees with the root conventionally labelled $0$ and $x0=1$, and let $mathsf{inv}(T)$ be the invers…

Let $n$ be a positive integer, let $mathsf{RTT}j(1^{n+1})$ denote the set of standard fully tiered rooted trees on $n+1$ vertices whose root is labelled $j$, and let…

Let $u$ be a composition, let $u( u)$ denote the partition obtained by rearranging its parts, and let $mathsf{RTT}(nu)$ be the set of fully tiered rooted trees associated with…

Let $p$ be a prime number, and let a modular form have odd weight and come from a Borcherds product. Odd-weight Borcherds-product conjecture. Any modular form of odd weight coming…

Let $\boldsymbol{K}$ be the Eisenstein field, let a Hermitian theta series be associated with the Hermitian Leech lattice, and let $p$ be a prime number. Hermitian Leech-lattice th…