On Numerical Semigroups with Almost-Maximal Genus

  • Joshua Arroyo Rose-Hulman Institute of Technology
  • Jackson Autry Texas A&M University
  • Charlotte Crandall Smith College
  • Jess Lefler Slippery Rock University
  • Vadim Ponomarenko San Diego State University
Keywords: semigroup; numerical set; genus; atom monoid

Abstract

A numerical semigroup is a cofinite subset of N0, containing 0, that is closed under addition.  Its genus is the number of nonnegative integers that are missing.  A numerical set is a similar object, not necessarily closed under addition.  If T is a numerical set, then A(T)={n in N0 : n+T is a subset of T} is a numerical semigroup.  Recently a paper appeared counting the number of numerical sets T where A(T) is a numerical semigroup of maximal genus.  We count the number of numerical sets T where A(T) is a numerical semigroup of almost-maximal genus, i.e. genus one smaller than maximal.

Published
2020-04-17
How to Cite
Arroyo, J., Autry, J., Crandall, C., Lefler, J., & Ponomarenko, V. (2020). On Numerical Semigroups with Almost-Maximal Genus. The PUMP Journal of Undergraduate Research, 3, 62-67. Retrieved from https://journals.calstate.edu/pump/article/view/2283