On the genus of a quotient of a numerical semigroup

  • Ayomikun Adeniran
  • Steve Butler
  • Colin Defant
  • Yibo Gao
  • Pamela E. Harris
  • Cyrus Hettle
  • Qingzhong Liang
  • Hayan NamEmail author
  • Adam Volk
Research Article


We find a relation between the genus of a quotient of a numerical semigroup S and the genus of S itself. We use this identity to compute the genus of a quotient of S when S has embedding dimension 2. We also exhibit identities relating the Frobenius numbers and the genus of quotients of numerical semigroups that are generated by certain types of arithmetic progressions.


Numerical semigroups Quotient of numerical semigroups Genus Frobenius numbers 



A. Adeniran, C. Defant, Y. Gao, C. Hettle, Q. Liang, H. Nam, and A. Volk were partially supported by NSF-DMS Grant #1603823 “Collaborative Research: Rocky Mountain Great Plains Graduate Research Workshops in Combinatorics” and by NSF-DMS Grant #1604458, “Collaborative Research: Rocky Mountain Great Plains Graduate Research Workshops in Combinatorics.” S. Butler and P. E. Harris were partially supported by NSA Grant #H98230-18-1-0017, “The 2018 and 2019 Rocky Mountain—Great Plains Graduate Research Workshops in Combinatorics.” C. Defant was also supported by a Fannie and John Hertz Foundation Fellowship and an NSF Graduate Research Fellowship.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ayomikun Adeniran
    • 1
  • Steve Butler
    • 2
  • Colin Defant
    • 3
  • Yibo Gao
    • 4
  • Pamela E. Harris
    • 5
  • Cyrus Hettle
    • 6
  • Qingzhong Liang
    • 7
  • Hayan Nam
    • 8
    Email author
  • Adam Volk
    • 9
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA
  3. 3.Department of MathematicsPrinceton UniversityPrincetonUSA
  4. 4.Department of MathematicsMITCambridgeUSA
  5. 5.Department of Mathematics and StatisticsWilliams CollegeWilliamstownUSA
  6. 6.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  7. 7.Department of MathematicsDuke UniversityDurhamUSA
  8. 8.Department of MathematicsUniversity of California, IrvineIrvineUSA
  9. 9.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

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