On the sets of lengths of Puiseux monoids generated by multiple geometric sequences
| Autor: | Polo, Harold |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4134/CKMS.c200017 |
| Popis: | In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids $M$ that are hereditarily atomic (i.e., every submonoid of $M$ is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers. Comment: 17 pages; in this new version we additionally prove that canonical rational multicyclic monoids satisfy the Structure Theorem for Unions of Sets of Lengths and offer a characterization of the elements of a rational multicyclic monoids that have finite set of lengths; moreover, we improve the exposition of the paper. This version will appear in Communications of the Korean Mathematical Society |
| Databáze: | arXiv |
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