Repetitions in beta-integers
Combinatorics
2013-02-12 v1
Abstract
Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of quasicrystals. We are interested in beta-integers realizing only a finite number of distinct distances between neighboring elements. In such a case, the problem may be reformulated in terms of combinatorics on words as a study of the index of infinite words coding beta-integers. We will solve a particular case for beta being a quadratic non-simple Parry number.
Keywords
Cite
@article{arxiv.0812.4006,
title = {Repetitions in beta-integers},
author = {L. Balková and K. Klouda and E. Pelantová},
journal= {arXiv preprint arXiv:0812.4006},
year = {2013}
}
Comments
11 pages