Abstract
We define a reflective numerical semigroup of genus as a numerical semigroup that has a certain reflective symmetry when viewed within as an array with columns. Equivalently, a reflective numerical semigroup has one gap in each residue class modulo . In this paper, we give an explicit description for all reflective numerical semigroups. With this, we can describe the reflective members of well-known families of numerical semigroups as well as obtain formulas for the number of reflective numerical semigroups of a given genus or given Frobenius number.
Dedication
This paper is dedicated to the memory of Dr. Emma Previato, my PhD advisor and friend.
Citation
Caleb M. Shor. "REFLECTIVE NUMERICAL SEMIGROUPS." Albanian J. Math. 17 (1) 41 - 68, 2023. https://doi.org/10.51286/albjm/1675941730
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