602 research outputs found
Uniformly balanced words with linear complexity and prescribed letter frequencies
We consider the following problem. Let us fix a finite alphabet A; for any
given d-uple of letter frequencies, how to construct an infinite word u over
the alphabet A satisfying the following conditions: u has linear complexity
function, u is uniformly balanced, the letter frequencies in u are given by the
given d-uple. This paper investigates a construction method for such words
based on the use of mixed multidimensional continued fraction algorithms.Comment: In Proceedings WORDS 2011, arXiv:1108.341
Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincar\'e Algorithm
The Arnoux-Rauzy-Poincar\'e multidimensional continued fraction algorithm is
obtained by combining the Arnoux-Rauzy and Poincar\'e algorithms. It is a
generalized Euclidean algorithm. Its three-dimensional linear version consists
in subtracting the sum of the two smallest entries to the largest if possible
(Arnoux-Rauzy step), and otherwise, in subtracting the smallest entry to the
median and the median to the largest (the Poincar\'e step), and by performing
when possible Arnoux-Rauzy steps in priority. After renormalization it provides
a piecewise fractional map of the standard -simplex. We study here the
factor complexity of its associated symbolic dynamical system, defined as an
-adic system. It is made of infinite words generated by the composition of
sequences of finitely many substitutions, together with some restrictions
concerning the allowed sequences of substitutions expressed in terms of a
regular language. Here, the substitutions are provided by the matrices of the
linear version of the algorithm. We give an upper bound for the linear growth
of the factor complexity. We then deduce the convergence of the associated
algorithm by unique ergodicity.Comment: 36 pages, 16 figure
Specular sets
We introduce the notion of specular sets which are subsets of groups called
here specular and which form a natural generalization of free groups. These
sets are an abstract generalization of the natural codings of linear
involutions. We prove several results concerning the subgroups generated by
return words and by maximal bifix codes in these sets.Comment: arXiv admin note: substantial text overlap with arXiv:1405.352
A Characterization of Infinite LSP Words
G. Fici proved that a finite word has a minimal suffix automaton if and only
if all its left special factors occur as prefixes. He called LSP all finite and
infinite words having this latter property. We characterize here infinite LSP
words in terms of -adicity. More precisely we provide a finite set of
morphisms and an automaton such that an infinite word is LSP if
and only if it is -adic and all its directive words are recognizable by
-adic expansions related to continued fractions (Natural extension of arithmetic algorithms and S-adic system)
"Natural extension of arithmetic algorithms and S-adic system". July 20ïœ24, 2015. edited by Shigeki Akiyama. The papers presented in this volume of RIMS KĂŽkyĂ»roku Bessatsu are in final form and refereed.We consider S-adic expansions associated with continued fraction algorithms, where an S-adic expansion corresponds to an infinite composition of substitutions. Recall that a substitution is a morphism of the free monoid. We focus in particular on the substitutions associated with regular continued fractions (Sturmian substitutions), and with Arnoux-Rauzy, Brun, and Jacobi{Perron (multidimensional) continued fraction algorithms. We also discuss the spectral properties of the associated symbolic dynamical systems under a Pisot type assumption
Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions
This paper studies tilings related to the beta-transformation when beta is a
Pisot number (that is not supposed to be a unit). Then it applies the obtained
results to study the set of rational numbers having a purely periodic
beta-expansion. Special focus is given to some quadratic examples
Adapting new materials for SLS: A case study
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Return words of linear involutions and fundamental groups
We investigate the natural codings of linear involutions. We deduce from the
geometric representation of linear involutions as Poincar\'e maps of measured
foliations a suitable definition of return words which yields that the set of
first return words to a given word is a symmetric basis of the free group on
the underlying alphabet . The set of first return words with respect to a
subgroup of finite index of the free group on is also proved to be a
symmetric basis of
Le Diamant â Dizac, premiĂšre approche de la cĂ©ramique
Le site de Dizac, situĂ© dans le sud-ouest de lâĂźle, est connu depuis 1962 et fut fouillĂ© par de nombreux chercheurs en particulier par M. Mattioni, J. Petitjean-Roget, H. Theuvenin et F. Turcat. Cependant, la nature de lâoccupation de ce site nâa pu ĂȘtre dĂ©terminĂ©e par les sondages effectuĂ©s. Les fouilles menĂ©es sous la responsabilitĂ© de Nathalie Vidal de 1989 Ă Â 1992 ont Ă©tĂ© rĂ©alisĂ©es de façon extensive, selon une mĂ©thode dâexcavation trĂšs fine, afin dâobtenir une meilleure vision dâensemble ..
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