On the sets of lengths of Puiseux monoids generated by multiple geometric sequences
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1057-1073
https://doi.org/10.4134/CKMS.c200017
Published online September 7, 2020
Printed October 31, 2020
Harold Polo
University of Florida
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
MSC numbers : Primary 20M13; Secondary 06F05, 20M14
Supported by : While work-ing on this manuscript, the author was supported by the University of Florida Mathematics Department Fellowship.
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