Numerical Semigroups on Compound Sequences. Issue 9 (1st September 2016)

• Record Type: Journal Article
• Authors: Kiers, Claire; O'Neill, Christopher; Ponomarenko, Vadim
• Is Part Of: Communications in algebra. Volume 44:Issue 9(2016)
• Page Start: 3842
• Page End: 3852
• Publication Date: 2016-09-01
• Subjects: Nonunique factorization -- Numerical semigroup; 20M13 -- 11A51 -- 20M14; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1087013
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : We generalize the geometric sequence { a p, a p −1 b, a p −2 b 2, …, b p } to allow the p copies of a (resp. b ) to all be different. We call the sequence { a 1 a 2 a 3 … a p, b 1 a 2 a 3 … a p, b 1 b 2 a 3 … a p, …, b 1 b 2 b 3 … 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.