The maximal denumerant of a numerical semigroup

numericalsgps, a GAP package for numerical semigroups

“…The maximal denumerant of s is the number of factorizations of s with maximal length. Even though the denumerant is not bounded while s increases in S, the maximal denumerant is finite and can be effectively computed ( [14]). We include this algorithm in the package as well as tests for supersymmetry and additiveness (see [14] for details).…”

An Overview of the Computational Aspects of Nonunique Factorization Invariants

“…If M is a numerical semigroup, set the maximal denumerant of M as the maximum of the maximal denumerants of elements of M . Bryant and Hamblin give in [6]…”

“…The problem is that this bound can be huge. gap> s:=NumericalSemigroup(701,902,1041); <Numerical semigroup with 3 generators> gap> DeltaSetOfNumericalSemigroup(s); [ 1,2,3,4,5,6,11,17 ] gap> DeltaSetPeriodicityBoundForNumericalSemigroup(s); 313436…”

“…6,6,7,7,7,8,8,9,9,9,10,10,11,11,12,12,12,14,13,14,15,15,16,16,17,17,18,19,19,20,20,21,22,22,23,24,24,25,26,26,27,28,29,29,30,31,31,33,33,34,35,35,37,37,…”

Classes of complete intersection numerical semigroups

“…In connection to this, the number of maximal representations of elements in a semigroup has been investigated recently (cf. [12], [13]). Now we give the criteria for the remaining classes.…”