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Minimal presentations of shifted numerical monoids

Algebra & Discrete Mathematics

Speaker: Chris O'Neill, Texas A&M Univ.
Location: 3106 MSB
Start time: Wed, May 18 2016, 5:10PM

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.