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- W3125564345 abstract "We study the cyclotomic exponent sequence of a numerical semigroup $S,$ and we compute its values at the gaps of $S,$ the elements of $S$ with unique representations in terms of minimal generators, and the Betti elements $bin S$ for which the set ${a in operatorname{Betti}(S) : a le_{S}b}$ is totally ordered with respect to $le_S$ (we write $a le_S b$ whenever $a - b in S,$ with $a,bin S$). This allows us to characterize certain semigroup families, such as Betti-sorted or Betti-divisible numerical semigroups, as well as numerical semigroups with a unique Betti element, in terms of their cyclotomic exponent sequences. Our results also apply to cyclotomic numerical semigroups, which are numerical semigroups with a finitely supported cyclotomic exponent sequence. We show that cyclotomic numerical semigroups with certain cyclotomic exponent sequences are complete intersections, thereby making progress towards proving the conjecture of Ciolan, Garcia-Sanchez and Moree (2016) stating that $S$ is cyclotomic if and only if it is a complete intersection." @default.
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- W3125564345 date "2021-01-21" @default.
- W3125564345 modified "2023-10-17" @default.
- W3125564345 title "Cyclotomic exponent sequences of numerical semigroups" @default.
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