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
India
Abstract:
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 n
∉ S but kn ∈ S
for each k ∈ Z, 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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