RT journal article
T1 Numerical semigroups that are not intersections of d-squashed semigroups
A1 Moreno Frías, María Ángeles
A1 Nicola, J
A1 Pardo Espino, Enrique
A1 Thomas, H
A2 Matemáticas
K1 Numerical Semigroups
K1 d-squashed semigroups
K1 proportionally modular numerical semigroup
AB We say that a numerical semigroup is d-squashed if it can be written in the formS =1/N(a1, . . . , ad) ∩ Zfor N, a1, . . . , ad positive integers with gcd(a1, . . . , ad) = 1. Rosales and Urbano have shown that anumerical semigroup is 2-squashed if and only if it is proportionally modular.Recent works by Rosales et al. give a concrete example of a numerical semigroup that cannotbe written as an intersection of 2-squashed semigroups. We will show the existence of infinitely manynumerical semigroups that cannot be written as an intersection of 2-squashed semigroups. We also willprove the same result for 3-squashed semigroups. We conjecture that there are numerical semigroupsthat cannot be written as the intersection of d-squashed semigroups for any fixed d, and we prove somepartial results towards this conjecture.
PB Cambridge
SN 0008-4395
YR 2009
FD 2009
LK http://hdl.handle.net/10498/35327
UL http://hdl.handle.net/10498/35327
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026