Factors of generalised polynomials and automatic sequences

被引：3
|
作者：
Byszewski, Jakub [2 ]
Konieczny, Jakub [1 ,2 ]
机构：
[1] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, IL-9190401 Jerusalem, Israel
[2] Jagiellonian Univ, Inst Math, Fac Math & Comp Sci, Ul Prof Stanislawa Lojasiewicza 6, PL-30348 Krakow, Poland
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2018年 / 29卷 / 03期
基金：
欧洲研究理事会;
关键词：
Generalised polynomials; Automatic sequences; Nilmanifolds;
D O I：
10.1016/j.indag.2018.03.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The aim of this short note is to generalise the result of Rampersad-Shallit saying that an automatic sequence and a Sturmian sequence cannot have arbitrarily long common factors. We show that the same result holds if a Sturmian sequence is replaced by an arbitrary sequence whose terms are given by a generalised polynomial (i.e., an expression involving algebraic operations and the floor function) that is not periodic except for a set of density zero. (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：981 / 985
页数：5
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