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Cyclotomic numerical semigroup polynomials with at most two irreducible factors.
- Source :
- Semigroup Forum; Dec2021, Vol. 103 Issue 3, p812-828, 17p
- Publication Year :
- 2021
-
Abstract
- A numerical semigroup S is cyclotomic if its semigroup polynomial P S is a product of cyclotomic polynomials. The number of irreducible factors of P S (with multiplicity) is the polynomial length ℓ (S) of S. We show that a cyclotomic numerical semigroup is complete intersection if ℓ (S) ≤ 2 . This establishes a particular case of a conjecture of Ciolan et al. (SIAM J Discrete Math 30(2):650–668, 2016) claiming that every cyclotomic numerical semigroup is complete intersection. In addition, we investigate the relation between ℓ (S) and the embedding dimension of S. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00371912
- Volume :
- 103
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Semigroup Forum
- Publication Type :
- Academic Journal
- Accession number :
- 153206385
- Full Text :
- https://doi.org/10.1007/s00233-021-10197-8