DOI QR코드

DOI QR Code

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

  • Polo, Harold (Department of Mathematics University of Florida)
  • 투고 : 2020.01.18
  • 심사 : 2020.07.20
  • 발행 : 2020.10.31

초록

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.

키워드

과제정보

The author wants to thank Felix Gotti for his guidance throughout the different stages of this manuscript and for many useful conversations about factorization theory. The author extends his thanks to anonymous referees whose feedback improve the final version of this paper. While working on this manuscript, the author was supported by the University of Florida Mathematics Department Fellowship.

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