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Numerical semigroups [electronic resource] : IMNS 2018 / Valentina Barucci, Scott Chapman, Marco D'Anna, Ralf Fröberg, editors.

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Bibliographic Details
Online Access: Full Text (via Springer)
Corporate Author: International Meeting on Numerical Semigroups Cortona, Italy
Other Authors: Barucci, Valentina, 1950-, Chapman, Scott, Fröberg, Ralf, D'Anna, Marco
Other title:IMNS 2018.
Format: Electronic Conference Proceeding eBook
Language:English
Published: Cham : Springer, 2020.
Series:Springer INdAM series ; v. 40.
Subjects:
Semigroups > Congresses.
Table of Contents:
  • Intro
  • Preface
  • Contents
  • Counting Numerical Semigroups by Genus and Even Gaps via Kunz-Coordinate Vectors
  • 1 Introduction
  • 2 Apéry Set and Kunz-Coordinate Vector
  • 3 The Main Result and an Application to a Counting Problem
  • References
  • Patterns on the Numerical Duplication by Their Admissibility Degree
  • 1 Introduction
  • 2 Preliminaries
  • 3 Patterns and Their Admissibility Degree
  • 4 Patterns Equivalent to the Arf Pattern
  • 5 Patterns on the Numerical Duplication
  • 6 Patterns on Rings
  • References
  • Primality in Semigroup Rings
  • 1 Introduction.
  • 2 Primal Elements in Monoids
  • 3 Primal Elements in a Graded Domain
  • 4 Primal Elements in Semigroup Rings
  • References
  • Conjecture of Wilf: A Survey
  • 1 Introduction
  • 1.1 Terminology and Notation
  • 1.2 A Convenient Way to Visualize Numerical Semigroups
  • 2 Two Problems Posed by Wilf
  • 2.1 Wilf's Paper
  • 2.2 Problem (a.i): Wilf's Conjecture
  • 2.3 Problem (a.ii): Another Open Problem
  • 2.4 Problem (b): Counting Numerical Semigroups
  • 3 Some Classes of Wilf Semigroups
  • 3.1 The Type as an Important Ingredient
  • 3.2 Semigroups Given by Sets of Generators.
  • 3.3 Semigroups with Nonnegative Eliahou Numbers
  • 3.4 Natural Constructions
  • 3.5 Semigroups with Small Multiplicity
  • 3.6 Semigroups with Large Embedding Dimension (Compared to the Multiplicity)
  • 3.6.1 Some Comments
  • 3.7 Semigroups with Big Multiplicity (and Possibly Small Embedding Dimension)
  • 3.8 Semigroups with Large Multiplicity (Compared to the Conductor)
  • 3.8.1 Some Comments
  • 3.9 Considering Unusual Invariants
  • 3.10 Families Described Through One Invariant
  • 4 Quasi-Generalization
  • References
  • Gapsets of Small Multiplicity
  • 1 Introduction
  • 2 Gapset Filtrations.
  • 2.1 The Canonical Partition
  • 2.2 Gapset Filtrations
  • 3 The Case m=3
  • 4 Some More General Tools
  • 4.1 On m-Extensions and m-Filtrations
  • 4.2 Gapset Filtrations Revisited
  • 4.3 A Compact Representation
  • 4.4 Complementing an m-Extension
  • 4.5 The Insertion Maps fi
  • 5 The Case m=4
  • 5.1 Concluding Remark
  • References
  • Generic Toric Ideals and Row-Factorization Matrices in Numerical Semigroups
  • 1 Preliminaries
  • 1.1 Numerical Semigroups
  • 1.2 The Fibers of Elements in Numerical Semigroups
  • 1.3 Semigroup Rings
  • 2 Generic Toric Ideals
  • 2.1 Main Results
  • 2.2 Basic Fibers.

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