3 papers
math.CO2026
On the smallest partition associated to a numerical semigroup
Nathan Kaplan, Kaylee Kim, Cole McGeorge +2
The set of hook lengths of an integer partition is the complement of some numerical semigroup . There has been recent interest in studying the number of partitions with a g…
math.CO2026
Ordinarization numbers of numerical semigroups
Sogol Cyrusian, Nathan Kaplan
There has been significant recent interest in studying how the number of numerical semigroups of genus behaves as a function of . Bras-Amorós has shown how to organize the…
math.NT2025
A Goldbach theorem for Laurent series semidomains
Nathan Kaplan, Harold Polo
A semidomain is a subsemiring of an integral domain. One can think of a semidomain as an integral domain in which additive inverses are no longer required. A semidomain is addi…