@misc{10498/35327,
year = {2009},
url = {http://hdl.handle.net/10498/35327},
abstract = {We say that a numerical semigroup is d-squashed if it can be written in the form
S =1/N(a1, . . . , ad) ∩ Z
for N, a1, . . . , ad positive integers with gcd(a1, . . . , ad) = 1. Rosales and Urbano have shown that a
numerical 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 cannot
be written as an intersection of 2-squashed semigroups. We will show the existence of infinitely many
numerical semigroups that cannot be written as an intersection of 2-squashed semigroups. We also will
prove the same result for 3-squashed semigroups. We conjecture that there are numerical semigroups
that cannot be written as the intersection of d-squashed semigroups for any fixed d, and we prove some
partial results towards this conjecture.},
publisher = {Cambridge},
keywords = {Numerical Semigroups},
keywords = {d-squashed semigroups},
keywords = {proportionally modular numerical semigroup},
title = {Numerical semigroups that are not intersections of d-squashed semigroups},
doi = {10.4153/CMB-2009-059-4},
author = {Moreno Frías, María Ángeles and Nicola, J and Pardo Espino, Enrique and Thomas, H},
}