Wilf's question in numerical semigroups S₃ revisited and inequalities for rescaled genera

2024/06/19 by Leonid G. Fel, Fel, Leonid G.
Mathematics · Decision Sciences · #Commutative Algebra and Its Applications #Scheduling and Timetabling Solutions #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2406.13580

Abstract

We consider numerical semigroups S₃ = ⟨ d₁,d₂,d₃⟩, minimally generated by three positive integers. We revisit the Wilf question in S₃ and, making use of identities for degrees of syzygies of such semigroups, give a short proof of existence of an affirmative answer. We find also the lower bound for Frobenius numbers of S₃ and upper and lower bounds for rescaled genera.

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