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In an atomic, cancellative, commutative monoid, the \omega-value measures howfar an element is from being prime. In numerical monoids, we show that thisinvariant exhibits eventual quasilinearity (i.e., periodic linearity). We applythis result to describe the asymptotic behavior of the \omega-function for ageneral numerical monoid and give an explicit formula when the monoid hasembedding dimension 2.

On the Linearity of \omega-primality in Numerical Monoids