Author, as appears in the article.: Bras-Amorós M
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Bras Amoros, Maria
Keywords: Msc: primary 00a65
Abstract: © 2019, © THE MATHEMATICAL ASSOCIATION OF AMERICA. We analyze the set of increasingly enumerable additive submonoids of R , for instance, the set of logarithms of the positive integers with respect to a given base. We call them ω-monoids. The ω-monoids for which consecutive elements become arbitrarily close are called tempered monoids. This is, in particular, the case for the set of logarithms. We show that any ω-monoid is either a scalar multiple of a numerical semigroup or a tempered monoid. We will also show how we can differentiate ω-monoids that are multiples of numerical semigroups from those that are tempered monoids by the size and commensurability of their minimal generating sets. All the definitions and results are illustrated with examples from music theory.
Thematic Areas: Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ciência da computação
licence for use: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 00029890
Author's mail: maria.bras@urv.cat
Author identifier: 0000-0002-3481-004X
Record's date: 2023-02-18
Papper version: info:eu-repo/semantics/acceptedVersion
Link to the original source: https://www.tandfonline.com/doi/abs/10.1080/00029890.2020.1674073?journalCode=uamm20
Papper original source: American Mathematical Monthly. 127 (1): 33-44
APA: Bras-Amorós M (2020). Increasingly Enumerable Submonoids of : Music Theory as a Unifying Theme. American Mathematical Monthly, 127(1), 33-44. DOI: 10.1080/00029890.2020.1674073
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Article's DOI: 10.1080/00029890.2020.1674073
Entity: Universitat Rovira i Virgili
Journal publication year: 2020
Publication Type: Journal Publications
Repositori URV