Please use this identifier to cite or link to this item:
acessibilidade
http://hdl.handle.net/20.500.12207/5968
Title: | The frobenius problem for generalized repunit numerical semigroups |
Authors: | Branco, Manuel B. Colaço, Isabel Ojeda, Ignacio |
Keywords: | Numerical semigroup Apéry sets Frobenius problem Genus Type Wilf conjeturee |
Issue Date: | 3-Dec-2022 |
Publisher: | Mediterrean Journal of Mathematics |
Citation: | Branco, M. B., Colaço, I., & Ojeda, I. (2022). The frobenius problem for generalized repunit numerical semigroups. Mediterranean Journal of Mathematics, 20(16), 1-18. https://doi.org/10.1007/s00009-022-02233-w |
Abstract: | In this paper, we introduce and study the numerical semigroups generated by {a1, a2, . . .} ⊂ N such that a1 is the repunit number in base b > 1 of length n > 1 and ai − ai−1 = a bi−2, for every i ≥ 2, where a is a positive integer relatively prime with a1. These numerical semigroups generalize the repunit numerical semigroups among many others. We show that they have interesting properties such as being homogeneous and Wilf. Moreover, we solve the Frobenius problem for this family, by giving a closed formula for the Frobenius number in terms of a, b and n, and compute other usual invariants such as the Ap´ery sets, the genus or the type. |
Peer reviewed: | yes |
URI: | https://hdl.handle.net/20.500.12207/5968 |
metadata.dc.identifier.doi: | https://doi.org/10.1007/s00009-022-02233-w |
ISSN: | 1660-5454 |
Publisher version: | http://link.springer.com/journal/9 |
Appears in Collections: | D-MCF - Artigos em revistas indexadas à WoS/Scopus |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
s00009-022-02233-w (3).pdf | 422.29 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License