Numerical semigroups from rational matrices III: semigroups of matricial dimension two and a counterexample to the lonely element conjecture

Abstract

We characterize semigroups in $\{0,1,2,\dots \}$ of matricial dimension $2$ and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonely has matricial dimension at most $2$.

arXiv comment15 pages