Approximating length-based invariants in atomic Puiseux monoids
A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization...
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2022
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1760 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543342393819136 |
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| author | Polo, H. |
| author_facet | Polo, H. |
| author_sort | Polo, H. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2022-06-15T04:49:44Z |
| description | A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization invariants of these two classes of monoids are related through a limiting process. This allows us to extend results from numerical to Puiseux monoids. We illustrate the versatility of this technique by recovering various known results about Puiseux monoids. |
| first_indexed | 2026-02-08T08:01:42Z |
| format | Article |
| id | admjournalluguniveduua-article-1760 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:42Z |
| publishDate | 2022 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-17602022-06-15T04:49:44Z Approximating length-based invariants in atomic Puiseux monoids Polo, H. atomic Puiseux monoids, numerical monoids, approximation, factorization invariants, sets of lengths, elasticity, set of distances Primary 20M13; Secondary 40A05, 20M14 A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization invariants of these two classes of monoids are related through a limiting process. This allows us to extend results from numerical to Puiseux monoids. We illustrate the versatility of this technique by recovering various known results about Puiseux monoids. Lugansk National Taras Shevchenko University 2022-06-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1760 10.12958/adm1760 Algebra and Discrete Mathematics; Vol 33, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1760/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1760/824 Copyright (c) 2022 Algebra and Discrete Mathematics |
| spellingShingle | atomic Puiseux monoids numerical monoids approximation factorization invariants sets of lengths elasticity set of distances Primary 20M13; Secondary 40A05 20M14 Polo, H. Approximating length-based invariants in atomic Puiseux monoids |
| title | Approximating length-based invariants in atomic Puiseux monoids |
| title_full | Approximating length-based invariants in atomic Puiseux monoids |
| title_fullStr | Approximating length-based invariants in atomic Puiseux monoids |
| title_full_unstemmed | Approximating length-based invariants in atomic Puiseux monoids |
| title_short | Approximating length-based invariants in atomic Puiseux monoids |
| title_sort | approximating length-based invariants in atomic puiseux monoids |
| topic | atomic Puiseux monoids numerical monoids approximation factorization invariants sets of lengths elasticity set of distances Primary 20M13; Secondary 40A05 20M14 |
| topic_facet | atomic Puiseux monoids numerical monoids approximation factorization invariants sets of lengths elasticity set of distances Primary 20M13; Secondary 40A05 20M14 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1760 |
| work_keys_str_mv | AT poloh approximatinglengthbasedinvariantsinatomicpuiseuxmonoids |