The Maximal Denumerant of a Numerical Semigroup
Abstract
Given a numerical semigroup S = <a0, a1, a2,..., at> and n in S, we consider the factorization n = c0 a0 + c1 a1 + ... + ct at where ci >= 0. Such a factorization is maximal if c0 + c1 + ... + ct is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.
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