5 problems

Let … be the multivariable exponential generating function for submonoids of products of finite commutative monoids. Rationality conjecture. The generating function $G(x,y,z)$ is a…

Let the single-theater game have escalation set $S=\{1,\dots,m\}$. Its misère quotient is the commutative monoid obtained by identifying positions that are interchangeable in every…

He–et al.'s conjecture. There is some $n\in\mathbb{N}$ such that $V^{\otimes n}$ contains a direct summand of the form $\operatorname{Ind}(W)$ for a $kG$-module $W$.

Cartan nonsingularity conjecture for controlled stabilizers. If $C(\mathbb C M)$ is nonsingular, then $C(kM)$ is nonsingular for every field $k$ of characteristic $p$.

Let $\mathcal{PODI}_n$ be the monoid of partial order-preserving or order-reversing permutations, let $\mathcal{POI}_n$ be the monoid of partial order-preserving permutations, and…