2026/04/29 by Salvatore Tringali, Kerou Wen, Keru Wen · 1 citation
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.CO #math.NT #math.RA #semigroups and automata theory
paper · pdf · doi:10.1112/tlm3.70030
openalex publication_date 2026/05/25 · openalex created_date 2026/05/26 · openalex updated_date 2026/08/01
Abstract If is a numerical semigroup (i.e., a cofinite subset of the non‐negative integers closed under addition), then the collection of all non‐empty subsets of forms a semigroup under the sumset operation induced by addition in . Moreover, if , then is a monoid with identity element , and the family of all subsets of containing is a submonoid of . We show that the automorphism group of is trivial, and the same holds for when . The proofs blend ideas from combinatorics and semigroup theory.