Results 51 to 60 of about 593 (116)
Powers in a class of A-strict standard episturmian words
, 2007 This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words, extending recent ...
Glen, Amy, Glen, A.
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Consecutive Power Occurrences in Sturmian Words
Comptes Rendus. MathématiqueWe show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by $10$ and this bound is optimal, extending a result of Rampersad, who proved that the bound $9 ...
Bell, Jason +2 more
doaj +1 more source
, 2007 In this paper, we survey the rich theory of infinite episturmian words which generalize to any finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two letters.
Justin, J. +5 more
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On the Fibonacci Tiling and its Modern Ramifications
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well‐known Fibonacci chain to explain some of them, with pointers to various generalisations as well as ...
Michael Baake +2 more
wiley +1 more source
Substitutions and their Generalisations
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and potentials.
Neil Mañibo
wiley +1 more source
A characterization of fine words over a finite alphabet
, 2006 To any infinite word t over a finite alphabet A we can associate two infinite words min (t) and max (t) such that any prefix of min (t) (resp. max (t)) is the lexicographically smallest (resp. greatest) amongst the factors of t of the same length. We say
Glen, Amy, Glen, A.
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Markoff–Lagrange spectrum of one‐sided shifts
Mathematika, Volume 70, Issue 3, July 2024.Abstract For the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order, and its solution is the fixed point of a substitution for the alternating lexicographic order.
Hajime Kaneko, Wolfgang Steiner
wiley +1 more source
Directive words of episturmian words: equivalences and normalization
, 2008 Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms.
Amy Glen +8 more
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A Characterization of Sturmian Words by Return Words
European Journal of Combinatorics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
Open and Closed Prefixes of Sturmian Words
, 2013 A word is closed if it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open.
Alessandro De Luca +4 more
core +1 more source