Integer Semigroups Associated with Dumont-Thomas Numeration Systems. (4th March 2014)

• Record Type: Journal Article
• Authors: Sirvent, Víctor F.
• Other Names: da Fonseca C. Academic Editor.; Glen A. Academic Editor.; Jorgensen P. E. Academic Editor.; Kelarev A. V. Academic Editor.; Lin C.-K. Academic Editor.
• Is Part Of: ISRN combinatorics. Volume 2014(2014)
• Publication Date: 2014-03-04
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Electronic journals; Periodicals; 511.6
• DOI: 10.1155/2014/275260
• Languages: English
• ISSNs: 2090-8911

Abstract

Abstract : Given a primitive substitution, we define different binary operations on infinite subsets of the nonnegative integers. These binary operations are defined with the help of the Dumont-Thomas numeration system; that is, a numeration system associated with the substitution. We give conditions for these semigroups to have an identity element. We show that they are not finitely generated. These semigroups define actions on the set of positive integers. We describe the orbits of these actions. We also estimate the density of these sets as subsets of the positive integers.