Normaliz：仿射幺半群和有理锥的算法

与代数统计相关的锥的Hilbert基的迭代计算

Challenging computations of Hilbert bases of cones associated with algebraic statistics

本文给出了由$5\times 5\times 3$列联表导出的幺半群正规的两个独立的计算证明，完成了Hibi和Ohsugi的分类.我们表明，Vlach的向量反证正规性的幺半群来自$6\times 4\times 3$列联表是唯一的最小这样的向量对称。最后，我们计算了$|N|=5$的半图面的非正规幺半群所对应的锥的全Hilbert基。这些计算基于LattE-4 ti 2和Normaliz包的扩展。

用于Normaliz的Macaulay 2接口

A Macaulay 2 interface for Normaliz

Normaliz是一个计算正规仿射幺半群的希尔伯特基和相关任务的工具。我们描述Macaulay 2接口到Normaliz。它使Normaliz可以在Macaulay 2中的monoid代数上进行操作，相反，使Macaulay 2成为Normaliz的前端。

Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid

If $\mathbb{F}$ is an ordered field and $M$ is a finite-rank torsion-free monoid, then one can embed $M$ into a finite-dimensional vector space over $\mathbb{F}$ via the inclusion $M \hookrightarrow \text{gp}(M) \hookrightarrow \mathbb{F} \otimes_{\mathbb{Z}} \text{gp}(M)$, where $\text{gp}(M)$ is the Grothendieck group of $M$. Let $\mathcal{C}$ be the class consisting of all monoids (up to isomorphism) that can be embedded into a finite-rank free commutative monoid. Here we investigate how the atomic structure and arithmetic properties of a monoid $M$ in $\mathcal{C}$ are connected to the com…

齐次幺半群代数及其正规化的希尔伯特级数之差

Difference of Hilbert series of homogeneous monoid algebras and their normalizations

本文研究齐次幺半群代数与其正规化的希尔伯特级数之差，证明在满足Serre条件(S2)时，前者的h-多项式次数不低于后者，并给出去掉该条件时的反例。

Atomicity of Positive Monoids

An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have been the subject of several recent papers. Moreover, those generated by a geometric sequence have also received a great deal of recent attention. Our purpose is to survey many of the recent advances regarding positive monoids, and we provide numerous examples to illustrate the complexity of their atomic and arithmetic structures.

代数锥

Algebraic cones

利用一维乘法代数幺半群${\bf M}_{\rm m}$和代数群${\bf G}_{\rm m}$的作用给出了代数锥的一个特征.