منابع مشابه
Syndeticity and independent substitutions
We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is the following. If a sequence x is generated by two independent substitutions — at least one being of exponential growth. Then the factors of x appearing infini...
متن کاملHigh density piecewise syndeticity of sumsets
Article history: Received 19 November 2013 Accepted 23 March 2015 Available online xxxx Communicated by H. Jerome Keisler MSC: 11B13 11B05 03H05 03H15
متن کاملA note on syndeticity, recognizable sets and Cobham's theorem
In this note, we give an alternative proof of the following result. Let p, q ≥ 2 be two multiplicatively independent integers. If an infinite set of integers is both pand q-recognizable, then it is syndetic. Notice that this result is needed in the classical proof of the celebrated Cobham’s theorem. Therefore the aim of this paper is to complete [13] and [1] to obtain an accessible proof of Cob...
متن کاملHigh density piecewise Syndeticity of Product Sets in Amenable Groups
M. Beiglböck, V. Bergelson, and A. Fish proved that if G is a countable amenable group and A and B are subsets of G with positive Banach density, then the product set AB is piecewise syndetic. This means that there is a finite subset E of G such that EAB is thick, that is, EAB contains translates of any finite subset of G. When G = Z, this was first proven by R. Jin. We prove a quantitative ver...
متن کاملSimple Sentences , Substitutions , and
Many competent speakers initially judge that (i) is true and (ii) is false, though they know that (iii) is true. (i) Superman leaps more tall buildings than Clark Kent. (ii) Superman leaps more tall buildings than Superman. (iii) Superman is identical with Clark Kent. Semantic explanations of these intuitions say that (i) and (ii) really can differ in truthvalue. Pragmatic explanations deny thi...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2009
ISSN: 0196-8858
DOI: 10.1016/j.aam.2008.02.001