Odd Right-End Numerical Semigroups Moreno Frías, María Ángeles Rosales González, José Carlos Frobenius number Frobenius variety Genus An odd right-end semigroup (hereinafter Ore semigroup) is a numerical semigroup S verifying that x + 1 ∈ S for every x ∈ S\{0} such that x is even. The introduction and study of these semigroups is the purpose of the present work. In particular, we will give some algorithms which compute all Ore semigroups with a given genus, a fixed Frobenius number and aspecific multiplicity. We will see that if X is a set of positive integers, then there exists the smallest Ore semigroup, under the inclusion sets, that contains X. We will denote this semigroup by θ[X] and present an algorithm to calculate it. Finally, we will study the embedding dimension, the Frobenius number, and the genus of Ore semigroups of the form θ[{m}], where m is a positive integer. As a consequence of this study, we will prove that this kind of semigroup satisfies Wilf’s conjecture. 2026-03-06T12:27:22Z 2026-03-06T12:27:22Z 2026-03-05 journal article Moreno-Frías, M. Á., & Rosales, J. C. (2026). Odd Right-End Numerical Semigroups. Axioms, 15(3), 189. https://doi.org/10.3390/axioms15030189 https://hdl.handle.net/10481/111941 10.3390/axioms15030189 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI