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Related papers: Numerical semigroups and applications

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We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most…

Algebraic Geometry · Mathematics 2007-11-16 Tristram de Piro

We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimension of numerical semigroups. We use these to compute the matricial dimension of every numerical semigroup with Frobenius number at most…

Combinatorics · Mathematics 2025-10-20 Theo Chinn , Junshu Feng , Stephan Ramon Garcia , Peiting Jiang

Good semigroups form a class of submonoids of $\mathbb{N}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the…

Combinatorics · Mathematics 2021-01-12 Lorenzo Guerrieri , Nicola Maugeri , Vincenzo Micale

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

Number Theory · Mathematics 2018-09-14 Gabor Wiese

This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…

Representation Theory · Mathematics 2019-09-24 Helmut Lenzing

This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…

Algebraic Geometry · Mathematics 2016-06-24 Tim Netzer

This paper determines almost symmetric numerical semigroups with maximal reduced type completely. In addition, this paper classifies MED-semigroups with maximal reduced type.

Commutative Algebra · Mathematics 2025-12-23 Akihiro Sugawara

We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…

Number Theory · Mathematics 2021-12-02 Matthew Just , Robert Schneider

Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to…

Commutative Algebra · Mathematics 2024-10-18 Pedro A. Garcia-Sanchez

We consider differential-algebraic equations in infinite dimensional state spaces and study, under which conditions we can associate a $C_{0}$-semigroup with such equations. We determine the right space of initial values and characterise…

Functional Analysis · Mathematics 2020-01-07 Sascha Trostorff

We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…

Combinatorics · Mathematics 2026-05-27 Alessio Moscariello , Alessio Sammartano

The purpose of this paper is to give an updated survey on various algebraic and analytic properties of semigroups related to fixed point properties of semigroup actions on a non-empty closed convex subset of a Banach space or, more…

Functional Analysis · Mathematics 2020-01-23 Anthony T. M. Lau , Yong Zhang

We generalize the geometric sequence $\{a^p, a^{p-1}b, a^{p-2}b^2,...,b^p\}$ to allow the $p$ copies of $a$ (resp. $b$) to all be different. We call the sequence $\{a_1a_2a_3\cdots a_p, b_1a_2a_3\cdots a_p, b_1b_2a_3\cdots a_p,\ldots,…

Commutative Algebra · Mathematics 2018-08-15 Claire Kiers , Christopher O'Neill , Vadim Ponomarenko

The present paper are the notes of a mini-course addressed mainly to non-experts. It purpose it to provide a first approach to the theory of mapping class groups of non-orientable surfaces.

Geometric Topology · Mathematics 2014-10-07 Luis Paris

This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…

Commutative Algebra · Mathematics 2015-03-19 J. I. García-García , M. A. Moreno-Frías , A. Vigneron-Tenorio

In this paper we extend some set theoretic concepts of numerical semigroups for arbitrary sub-semigroups of natural numbers. Then we characterized gapsets which leads to a more efficient computational approach towards numerical semigroups…

Combinatorics · Mathematics 2024-08-06 Arman Ataei Kachouei , Farhad Rahmati

In this paper we study numerical semigroups containing a given positive integer and closed with respect to the action of an affine map. For such semigroups we find a minimal set of generators, their embedding dimension, their genus and…

Number Theory · Mathematics 2018-06-12 Simone Ugolini

In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of…

Commutative Algebra · Mathematics 2025-11-25 Jonathan Chappelon , Jorge L. Ramírez Alfonsín , Dumitru I. Stamate

These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…

Mathematical Physics · Physics 2020-11-04 Nima Moshayedi

Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…

Group Theory · Mathematics 2025-05-02 Marcel Wild