Numerical Semigroups on Compound Sequences

Abstract

We generalize the geometric sequence {a^p, a^p−1b, a^p−2b²,…, b^p} to allow the p copies of a (resp. b) to all be different. We call the sequence {a₁a₂a₃… a_p, b₁a₂a₃…a_p, b₁b₂a₃…a_p,…, b₁b₂b₃…b_p} 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.

Key Words:

• Nonunique factorization
• Numerical semigroup

2010 Mathematics Subject Classification:

• 20M13
• 11A51
• 20M14