Numerical Semigroups on Compound Sequences

Abstract

We generalize the geometric sequence {ap, ap−1b, ap−2b2,…, bp} to allow the p copies of a (resp. b) to all be different. We call the sequence {a1a2a3… ap, b1a2a3…ap, b1b2a3…ap,…, b1b2b3…bp} a compound sequence. We consider numerical semigroups whose minimal set of generators form a compound sequence, and compute various semigroup and arithmetical invariants, including the Frobenius number, Apéry sets, Betti elements, and catenary degree. We compute bounds on the delta set and the tame degree.