On the linearity of ω-primality in numerical monoids |
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Authors: | Christopher O'Neill Roberto Pelayo |
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Institution: | 1. Mathematics Department, Duke University, Durham, NC 27708, United States;2. Mathematics Department, University of Hawai‘i at Hilo, Hilo, HI 96720, United States |
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Abstract: | In an atomic, cancellative, commutative monoid, the ω-value measures how far an element is from being prime. In numerical monoids, we show that this invariant exhibits eventual quasilinearity (i.e., periodic linearity). We apply this result to describe the asymptotic behavior of the ω-function for a general numerical monoid and give an explicit formula when the monoid has embedding dimension 2. |
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Keywords: | 06F05 11Y05 11Y11 11A51 |
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