Ciolan–García-Sánchez–Moree conjecture on cyclotomic numerical semigroups
A numerical semigroup is an additive submonoid of with finite complement in . It is cyclotomic if its semigroup polynomial is a product of cyclotomic polynomials, and it is complete intersection in the standard sense for numerical semigroups.
Ciolan–García-Sánchez–Moree conjecture. A numerical semigroup is cyclotomic if and only if it is complete intersection.
Complete intersection numerical semigroups are cyclotomic, so the conjecture asserts the converse implication. The source presents this as an open conjecture.
References
Primary source
Alessio Borzì, Andrés Herrera-Poyatos and Pieter Moree, “Cyclotomic numerical semigroup polynomials with at most two irreducible factors”, arXiv:2101.08823 (2021).
Additional references
3 papers in this index state this conjecture (2017–2021). The statement above is taken from the most recent of them; the others are arXiv:2005.09708, arXiv:1707.00782.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.