On the parameters of Algebraic Geometry codes related to Arf semigroups

Irreducibility of Arf Numerical Semigroups

In this paper, we introduce the concept of Arf special gaps of an Arf numerical semigroup, and an algorithm for computing all Arf special gaps of a given Arf numerical semigroup. We introduce the concept of Arf-irreducible numerical semigroups, and draw conclusions about all these concepts. We give a system of generators for the Frobenius variety and variety of families of Arf numerical semigroups. Moreover, we obtain the minimal Arf system of generators of a given Arf numerical semigroup.

Numerical Semigroups and Codes

A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes. We present these applications and some theoretical problems related to classification, characterization and counting of numerical semigroups.

预周期点、有限性以及代数态射半群的结构

Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms

本文利用 p-adic arc 方法探讨态射预周期点的有限性问题，证明了自同构群元素公共预周期点与群结构性质的联系，以及有限态射的 Northcott 型结果。

Applications of the Graph Minor Theorem to algebraic structures I

We use the Graph Minor Theorem to characterize infinite sequences of finite subsets of factorial and commutative semigroups (here semigroups have a unity element), e.g. the multiplicative semigroup of a unique factorization domain.

关于高维积分性和乘法依赖在半群代数动力学中的研究

On higher dimensional integrality and multiplicative dependence in semigroup algebraic dynamics

本文研究高维半群轨道中点的乘法依赖性，证明了半群轨道中积分点非密集性导致轨道中乘法依赖性稀疏，扩展了Bérczes等人和Northcott、Siegel定理的结果。

On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics

We consider semigroup dynamical systems defined by several polynomials over a number field $\mathbb{K}$, and the orbit (tree) they generate at a given point. We obtain finiteness results for the set of preperiodic points of such systems that fall in the cyclotomic closure of $\mathbb{K}$. More generally, we consider the finiteness of initial points in the cyclotomic closure for which the orbit contains an algebraic integer of bounded house. This work extends previous results for classical obits generated by one polynomial over $\mathbb{K}$ obtained initially by Dvornicich and Zannier (for prep…