Equidistribution of numerical semigroup gaps modulo m |
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Institution: | Department of Mathematics, Western New England University, Springfield, MA 01119, United States of America |
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Abstract: | For a positive integer m, a finite set of integers is said to be equidistributed modulo m if the set contains an equal number of elements in each congruence class modulo m. In this paper, we consider the problem of determining when the set of gaps of a numerical semigroup S is equidistributed modulo m. Of particular interest is the case when the nonzero elements of an Apéry set of S form an arithmetic sequence. We explicitly describe such numerical semigroups S and determine conditions for which the sets of gaps of these numerical semigroups are equidistributed modulo m. |
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Keywords: | Numerical semigroups Gaps Generalized arithmetic sequences Apéry sets |
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