https://hdl.handle.net/10481/41332 2026-04-06T06:19:34Z https://hdl.handle.net/10481/106123 The extended Frobenius problem for r-Fibonacci sequences shifted by r-Fibonacci numbers Robles Pérez, Aureliano M.; Rosales González, José Carlos Using properties of the generalised Zeckendorf decompositions, we study the extended Frobenius problem for sequences of the form $\{p_a+p_n\}_{n\in\mathbb{N}}$, where $\{p_n\}_{n\in\mathbb{N}}$ is an $r$-Fibonacci sequence and $p_a$ is an $r$-Fibonacci number. https://hdl.handle.net/10481/90624 The isomorphism problem for ideal class monoids of numerical semigroups García Sánchez, Pedro Abelardo From any poset isomorphic to the poset of gaps of a numerical semigroup S with the order induced by S, one can recover S. As an application, we prove that two different numerical semigroups cannot have isomorphic posets (with respect to set inclusion) of ideals whose minimum is zero. We also show that given two numerical semigroups S and T, if their ideal class monoids are isomorphic, then S must be equal to T. The author is partially supported by the grant number ProyExcel_00868 (Proyecto de Excelencia de la Junta de Andalucía) and by the Junta de Andalucía Grant Number FQM--343. He also acknowledges financial support from the grant PID2022-138906NB-C21 funded by MICIU/AEI/10.13039/501100011033 and by ERDF "A way of making Europe'', and from the Spanish Ministry of Science and Innovation (MICINN), through the "Severo Ochoa and María de Maeztu Programme for Centres and Unities of Excellence'' (CEX2020-001105-M). Funding for open access charge: Universidad de Granada / CBUA. https://hdl.handle.net/10481/90041 Numerical semigroups with monotone Apéry set and fixed multiplicity and ratio Robles Pérez, Aureliano M.; Rosales González, José Carlos We characterise the numerical semigroups with a monotone Apéry set (MANSsemigroups for short). Moreover, we describe the families ofMANS-semigroups when we fix the multiplicity and the ratio. https://hdl.handle.net/10481/81834 The extended Frobenius problem for Fibonacci sequences incremented by a Fibonacci number Robles Pérez, Aureliano M.; Rosales González, José Carlos We study the extended Frobenius problem for sequences of the form {fa+fn}n∈N, where {fn}n∈N is the Fibonacci sequence and fa is a Fibonacci number. As a consequence of this study, we show that the family of numerical semigroups associated with these sequences satisfies Wilf’s conjecture. https://hdl.handle.net/10481/80403 A Frobenius problem suggested by prime k-tuplets Robles Pérez, Aureliano M.; Rosales González, José Carlos We study the Frobenius problem for certain k-tuplets, which include prime k-tuplets. Moreover, we analyze some properties of the numerical semigroups associated with these tuplets.