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http://dx.doi.org/10.4134/CKMS.c200017

ON THE SETS OF LENGTHS OF PUISEUX MONOIDS GENERATED BY MULTIPLE GEOMETRIC SEQUENCES  

Polo, Harold (Department of Mathematics University of Florida)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.4, 2020 , pp. 1057-1073 More about this Journal
Abstract
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.
Keywords
Puiseux monoids; factorization theory; factorization invariants; set of lengths; union of sets of lengths; set of distances; delta set;
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