A computational approach to the study of finite-complement submonids of an affine cone

2024/09/10 by J. C. Rosales, Rosales, J. C., R. Tapia-Ramos +3 · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Differential Equations and Numerical Methods #Elasticity and Wave Propagation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2409.06376

openalex publication_date 2024/09/10 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

Let C⊆ ℕ^p be an integer cone. A C-semigroup S⊆ C is an affine semigroup such that the set C∖ S is finite. Such C-semigroups are central to our study. We develop new algorithms for computing C-semigroups with specified invariants, including genus, Frobenius element, and their combinations, among other invariants. To achieve this, we introduce a new class of C-semigroups, termed B-semigroups. By fixing the degree lexicographic order, we also research the embedding dimension for both ordinary and mult-embedded ℕ²-semigroups. These results are applied to test some generalizations of Wilf's conjecture.

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• On some affine semigroups characterized by a finite-state automata
• Affine semigroups without consecutive small elements

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