An extension of Wilf's conjecture to affine semigroups

2016/08/30 by J. I. García-García, García-García, J. I., D. Marín-Aragón +3 · 4 citations
Engineering · Mathematics · #05A15 #20M14 #68R05 #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras #Scheduling and Optimization Algorithms

paper · pdf · doi:10.48550/arxiv.1608.08528

openalex publication_date 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \CaC⊂ \Q^p be a rational cone. An affine semigroup S⊂ \CaC is a \CaC-semigroup whenever (\CaC∖ S)∩ \N^p has only a finite number of elements. In this work, we study the tree of \CaC-semigroups, give a method to generate it and study their subsemigroups with minimal embedding dimension. We extend Wilf's conjecture for numerical semigroups to \CaC-semigroups and give some families of \CaC-semigroups fulfilling the extended conjecture. We also check that other conjectures on numerical semigroups seem to be also satisfied by \CaC-semigroups.

Cited by

• On some affine semigroups characterized by a finite-state automata
• Buchsbaumness of finite complement simplicial affine semigroups
• Symmetric generalized numerical semigroups in ℕ^d with embedding dimension 2d+1
• The weak normalization of an affine semigroup

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