# Mathematics Colloquia and Seminars

Consider the family of numerical monoids $S_n = \langle n, n + r_1, \ldots, n + r_k \rangle$ obtained by varying $n$. In this talk, we exhibit periodic behavior of the minimal presentations of $S_n$ when $n$ is sufficiently large. As a consequence, we obtain eventual periodicity results for several arithmetic quantities arising in factorization theory.