5 problems

Wheeling conjecture. Wheeling intertwines the two products on Chinese characters; more precisely,

Let $B$ be the graded algebra under consideration, let $B_\psi=B/\langle b-\psi(b)\mid b\in B\rangle$, and let $C$ be the graded vector space with basis $v_d$ for…

Let $\mathsf{D}_{{\mathfrak S}(n)}$ be the diagrammatic representation-theoretic object associated with the symmetric group ${\mathfrak S}(n)$, and let $\mathsf{P}^{(n)}$ be its id…

Let $I$ be the vertex set of the Dynkin diagram. For $i\in I$ and $k\in\mathbb{N}$, let $c_k^i$ be a clockwise circle labeled $i$ containing exactly $k$ hollow dots, and let $c_k$…

Let $\lambda\rightarrow\ru(n,d)$ be arbitrary, and let $mu\rightarrow\ru(n,d)$ be obtained from $\lambda$ by moving all zero entries to the end while preserving the relative order of…