Nef-partitions arising from unimodular configurations

关于光滑良构Fano加权完全交的nef-分划的存在性

On the existence of nef-partitions for smooth well-formed Fano weighted complete intersections

该研究针对光滑良构Fano加权完全交的强nef-分划存在性猜想，证明余维数大于3时强nef-分划可能不存在，给出其存在的充分组合条件，并指出此类完全交的组合结构可任意复杂。

A regular unimodular triangulation of reflexive 2-supported weighted projective space simplices

For each integer partition $\mathbf{q}$ with $d$ parts, we denote by $Δ_{(1,\mathbf{q})}$ the lattice simplex obtained as the convex hull in $\mathbb{R}^d$ of the standard basis vectors along with the vector $-\mathbf{q}$. For $\mathbf{q}$ with two distinct parts such that $Δ_{(1,\mathbf{q})}$ is reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in $Δ_{(1,\mathbf{q})}$. We then construct a Gröbner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular un…

Ehrhart-equivalent $\boldsymbol 3$-polytopes are equidecomposable

We show that if two lattice $3$-polytopes $P$ and $P'$ have the same Ehrhart function then they are $\operatorname{GL}_3({\mathbb Z})$-equidecomposable; that is, they can be partitioned into relatively open simplices $U_1,\dots, U_k$ and $U'_1,\dots,U'_k$ such that $U_i$ and $U'_i$ are unimodularly equivalent, for each $i$.

序多面体与链多面体的边定理的改进

A refinement of the edge theorem for order and chain polytopes

本文改进序多面体与链多面体的边定理，通过连通凸子集划分边并证明对应类基数相等，给出边数闭式公式，并揭示已知双射的结构，同时比较边方向、边长与直径，讨论对组合优化的影响。