Journal of Integer Sequences, Vol. 24 (2021), Article 21.2.3

Some Results on Fundamental Gaps in Numerical Semigroups

Edgar Federico Elizeche and Amitabha Tripathi
Department of Mathematics
Indian Institute of Technology
Hauz Khas
New Delhi 110016


A numerical semigroup is a submonoid of Z≥0 whose complement in Z≥0 is finite. The gap set G(S) of a numerical semigroup S is the finite set Z≥0 \ S. A positive integer n is in the set FG(S) of fundamental gaps of S provided nS but knS for each kZ, k > 1. We explore the set FG(S) mostly when S is generated by two or three integers, but also in some other special cases, including when S is generated by arithmetic progressions.

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Received August 19 2020; revised versions received January 21 2021; January 24 2021; January 25 2021. Published in Journal of Integer Sequences, January 25 2021.

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