TY - JOUR AU - Joshua Arroyo AU - Jackson Autry AU - Charlotte Crandall AU - Jess Lefler AU - Vadim Ponomarenko PY - 2020/04/17 Y2 - 2024/03/29 TI - On Numerical Semigroups with Almost-Maximal Genus JF - The PUMP Journal of Undergraduate Research JA - PUMP J. Undergrad. Res. VL - 3 IS - 0 SE - Articles DO - 10.46787/pump.v3i0.2283 UR - https://journals.calstate.edu/pump/article/view/2283 AB - 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. ER -