On additive properties of sets defined by the Thue-Morse word. - UTU Research Portal

A1 Refereed original research article in a scientific journal

On additive properties of sets defined by the Thue-Morse word.

Authors: M Bucci, N Hindman, S Puzynina, L Q Zamboni

Publisher: elsevier

Publication year: 2013

Journal: Journal of Combinatorial Theory, Series A

Number in series: 6

Volume: 120

Issue: 6

First page : 1235

Last page: 1245

Number of pages: 11

ISSN: 0097-3165

DOI: https://doi.org/10.1016/j.jcta.2013.03.005(external)

Abstract

In this paper we study additive properties of subsets of the set of positive integers which we call finite and infinite FS-big. We prove that the finite FS-big property is partition regular, while the property of infinite FS-big is not. Besides that, we completely characterize additive properties of sets defined by occurrences of factors in the Thue-Morse word.