@article{Arroyo_Autry_Crandall_Lefler_Ponomarenko_2020, title={On Numerical Semigroups with Almost-Maximal Genus}, volume={3}, url={https://journals.calstate.edu/pump/article/view/2283}, abstractNote={<p>A numerical semigroup is a cofinite subset of <em>N</em><sub>0</sub>, 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 <em>T</em> is a numerical set, then <em>A(T)</em>={<em>n</em> in <em>N</em><sub>0 </sub>: <em>n+T</em> is a subset of <em>T</em>} is a numerical semigroup. Recently a paper appeared counting the number of numerical sets <em>T</em> where <em>A(T)</em> is a numerical semigroup of maximal genus. We count the number of numerical sets<em> T</em> where <em>A(T)</em> is a numerical semigroup of almost-maximal genus, i.e. genus one smaller than maximal.</p>}, journal={The PUMP Journal of Undergraduate Research}, author={Arroyo, Joshua and Autry, Jackson and Crandall, Charlotte and Lefler, Jess and Ponomarenko, Vadim}, year={2020}, month={Apr.}, pages={62-67} }