12 problems

Extended Wilf conjecture. The inequality

A finite rational cone is a cone generated by finitely many rational vectors, and its Hilbert basis is the canonical finite generating set of the associated affine semigroup. A sim…

Affine stratification conjecture. Every squarefree lattice game possesses an affine stratification.

Let $S$ be the affine semigroup considered in the paper, let $\bar S$ be its neighborhood complex, and let $\Lambda$ be the lattice containing $S$. A point $b$ is a neighbor of the…

Cisto's Generalized Wilf conjecture. The inequality

Monotonicity conjecture for B-semigroups. For any integer cone $\mathcal{C}\subseteq\mathbb{N}^p$ and any non-zero $g\in\mathbb{N}$,

Let $n\geq 2$, let $M=\mathbf P(n,\mathbb N)$, and let $S$ be a unipotent numerical monoid in $M$. Let $\varphi(S)$ be its image in $\mathbb N^{n-1}$ under the monoid isomorphism…

Let $\mathcal{C}$ be an integer cone such that the dimension of the real vector space generated by $\mathcal{C}$ is $p$. A $\mathcal{C}$-semigroup is an affine semigroup whose comp…

Affine stratification conjecture. Every squarefree lattice game, under normal play, ordinary misère play, or the more general misère play allowed by the axioms of lattice games, po…

Let $W$ be the set of winning positions of a lattice game. An affine stratification of $W$ is an expression of $W$ as a finite union of translates of affine semigroups. The affine…

Affine-stratification conjecture. Every lattice game possesses an affine stratification.

Sturmfels's conjecture. The systems in this family all have the same number of linearly independent solutions precisely when the corresponding affine semigroup ring is Cohen–Macaul…