2008/12/21 by Ľubomíra Balková, L. Balková, Karel Klouda +3 · 1 citation
Computer Science · Materials Science · Mathematics · #BETA (programming language) #Cellular Automata and Applications #Combinatorics #Computer science #Discrete mathematics #Geometry #Mathematics #Quadratic equation #Quasicrystal Structures and Properties #math.CO #msc:68R15 #semigroups and automata theory
paper · pdf · doi:10.1007/s11005-009-0301-z
published as Letters in Mathematical Physics 87 (2009), 181-195 · 11 pages
arxiv created 2008/12/21 · openalex publication_date 2009/01/27 · arxiv updated 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.