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ASYMPTOTIC BEHAVIOUR OF THE MAXIMAL NUMBER OF SQUARES IN STANDARD STURMIAN WORDS

MARCIN PIATKOWSKI, WOJCIECH RYTTER
2012 International Journal of Foundations of Computer Science  
The subject of computing maximal number of squares and repetitions in words is one of the fundamental topics in combinatorics on words [18, 22] initiated by A.  ...  A square in a string is a subword of the form ww, where w is nonempty.  ...  In this paper we concentrate on the asymptotic behaviour of the maximal number of squares in class of standard Sturmian words S.  ... 
doi:10.1142/s012905411240014x fatcat:ovjdjf4ufrbdvjyehyeadu6ifi

On extremal properties of the Fibonacci word

Julien Cassaigne
2008 RAIRO - Theoretical Informatics and Applications  
We survey several quantitative problems on infinite words related to repetitions, recurrence, and palindromes, for which the Fibonacci word often exhibits extremal behaviour.  ...  There exist binary words without long squares [16] , but a word without long squares may still have asymptotic index 2.  ...  The asymptotic index for Sturmian words was computed by Vandeth [29] (actually, the theorem is stated there only for Sturmian words that are fixed points of substitutions, but it remains valid in general  ... 
doi:10.1051/ita:2008003 fatcat:kzykr3odoncyzk2pyvqp6ip3ie

Strong Repetitions in Sturmian Strings [article]

Ayse Karaman
2011 arXiv   pre-print
In this paper, we analyze the periodic factors of Sturmian words for the findings to lead to a linear-time algorithm for the computation of runs in this class of words which, to our best knowledge, is  ...  an open problem in literature.  ...  [PR09] use the results in [DL03] to study the asymptotic behaviour of squares in Sturmian words.  ... 
arXiv:1002.4598v2 fatcat:uylmydslxrfupc3jryzwzq3bfq

Quantum chemistry with Coulomb Sturmians: Construction and convergence of Coulomb Sturmian basis sets at Hartree-Fock level [article]

Michael F. Herbst and James Emil Avery and Andreas Dreuw
2018 arXiv   pre-print
For example, an unusually large limit for the angular momentum quantum number in unrestricted Hartree-Fock calculations can be linked to the breaking of spherical symmetry in such cases.  ...  The proposed basis set construction selects Coulomb Sturmian functions using separate upper limits to their principle, angular momentum and magnetic quantum numbers.  ...  Herbst wishes to express his thanks to all members of the group of Prof. Dr. Brian Vinter at the Niels Bohr Institute for the hospitality and many fruitful discussions during visits.  ... 
arXiv:1811.05777v1 fatcat:olbl25c62fadtnyyh5773mwbce

Master index volumes 211–220

1999 Theoretical Computer Science  
of Sturmian sequences 218 (1) (1999) 3-12 of Sturmian words 218 (1) (1999) 83-94 Cattaneo, G., E.  ...  ., On the combinatorics of finite words 218 (1) (1999) 13-39 Delorme, M., J. Mazoyer and L.  ...  Terrier, Signals in one-dimensional cellular automata 217 (1) (1999)  ... 
doi:10.1016/s0304-3975(99)00145-0 fatcat:eo3pwtecv5cghidlyiykq6pioa

Spiked and 𝒫𝒯-symmetrized decadic potentials supporting elementaryN-plets of bound states

Miloslav Znojil
2000 Journal of Physics A: Mathematical and General  
The strong asymptotic growth of V(x) implies an ambiguity in the PT-symmetric quantization via complex boundary conditions but the three eligible recipes coincide at our exceptional solutions.  ...  We show that the potential wells with a central spike V(x) = x^10 + a x^8 + b x^6+ c x^4 + d x^2 + f/x^2 possess arbitrary finite multiplets of elementary exact bound states.  ...  The picture will be completed in what follows. We are going to demonstrate that a PT symmetrization of eq. (2) leads still to the maximal, type-I form of the QES property.  ... 
doi:10.1088/0305-4470/33/38/313 fatcat:bhiktqame5bfhimdcfp3krl3fe

COMBINATORICS ON WORDS – A TUTORIAL [chapter]

JEAN BERSTEL, JUHANI KARHUMÄKI
2004 Current Trends in Theoretical Computer Science  
Shallit for their careful reading of parts of a preliminary version of the paper. In addition the authors are grateful to A. Lepistö for his help to complete the presentation.  ...  A beautiful theorem, proved in [CMPS93] , describes those irrational numbers α for which the standard Sturmian word can be generated by iterating a morphism.  ...  The following numbers coincide (i) the maximal of free ranks of solutions of u = v in A * , (ii) the maximal of prefix ranks of solutions of u = v in A * , (iii) the maximal of combinatorial ranks of solutions  ... 
doi:10.1142/9789812562494_0059 fatcat:rb3muz6tsffbrpm26j4aj2rkey

New types of solvability in PT symmetric quantum theory

Miloslav Znojil
2005 arXiv   pre-print
The characteristic anti-linear (parity/time reversal, PT) symmetry of non-Hermitian Hamiltonians with real energies is presented as a source of two new forms of solvability of Schrödinger's bound-state  ...  In a broader context, speculations are added concerning possible relationship between PT symmetry, solvability and superintegrability.  ...  In fact, our states form the Sturmian L−plets (numbered by N = 0, 1, . . .) at charges F N,k numbered by k = 1, 2, . . . , L where L = D − 2 + 2m is N −independent.  ... 
arXiv:math-ph/0501058v1 fatcat:y2ea5h3zlbasbf37anpbiba5ne

Simple Toeplitz subshifts: combinatorial properties and uniformity of cocycles [article]

Daniel Sell
2020 arXiv   pre-print
This approach allows us to establish uniformity of cocycles for simple Toeplitz subshifts and Sturmian subshifts in a unified way.  ...  This generalises a result of Grigorchuk, Lenz and Nagnibeda from 2018. In addition the spectrum is shown to be a Cantor set of Lebesgue measure zero.  ...  Let # u (v) denote the maximal number of nonoverlapping copies of u in v.  ... 
arXiv:2006.15348v1 fatcat:7wmm667soba2fjpohrdvb337vm

Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081)

Maxime Crochemore, Lila Kari, Mehryar Mohri, Dirk Nowotka, Marc Herbstritt
2011 Dagstuhl Reports  
Scientists working in the fields of Combinatorics on Words, Computational Biology, Stringology, Natural Computing, and Machine Learning were invited to consider the seminar's topic from a wide range of  ...  They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words over, for example, the latin alphabet), in the process of  ...  The repetition threshold on k letters, RT (k), is the rational number γ k such that the number of γ + k -free k-ary words is infinite, while the number of γ k -free k-ary words is only finite.  ... 
doi:10.4230/dagrep.1.2.47 dblp:journals/dagstuhl-reports/CrochemoreKMN11 fatcat:s3v55bqr4fbdfo5kztirfoljqm

Breaking Time Reversal Symmetry in Chaotic Driven Rydberg Atoms

Krzysztof Sacha, Jakub Zakrzewski, Dominique Delande
2000 Annals of Physics  
mixes the various states inside an hydrogenic manifold of fixed principal quantum number.  ...  For some configurations of the fields, the classical secular motion (i.e. evolution in time of the elliptical electronic trajectory) is shown to be predominantly chaotic.  ...  ACKNOWLEDGMENTS We are grateful to Felix Izrailev for the permission to use his code for his NNS distribution. We thank the referee for bringing Refs. [56 58]  ... 
doi:10.1006/aphy.2000.6051 fatcat:oqux5qx74nebvkjs7vri3vcpca

Spectral triples for subshifts [article]

Antoine Julien, Ian F. Putnam
2015 arXiv   pre-print
The C*-algebra of this dynamical system is generated by functions in C(X) and a unitary element u implementing the action.  ...  Building on ideas of Christensen and Ivan, we give a construction of a family of spectral triples on the commutative algebra C(X).  ...  Acknowledgments Substantial part of this work was done while A. Julien was working at the University of Victoria, funded in part by the Pacific Institute for the Mathematical Sciences (PIMS).  ... 
arXiv:1411.6800v2 fatcat:w5vmdpa6craajoxbziou3dediy

Subject index volumes 101–150

1995 Theoretical Computer Science  
mentioned in this Subject Index refer to the Reference List of Indexed Articles (pp. 315-338 of this issue).  ...  of N 283 squared N 778 syntactic N 283 Ershov numerations 313 escape mechanisms 49 Estelle specifications 179 estimated maximal number 37 estimation 283, 385 algorithm 228 methods of N 283 query  ... 
doi:10.1016/0304-3975(95)90001-2 fatcat:omihw2cp6vb2hgwdfiksnt4ftu

Quantum chaos and analytic structure of the spectrum

W. D. Heiss, A. A. Kotzé
1991 Physical Review A. Atomic, Molecular, and Optical Physics  
The same behaviour is seen in a pure quantum one dimensional system consisting of a square well containing δ-function barriers on a Cantor set.  ...  This means that a GOE, which has no physical input a priori, only simulates the behaviour of a chaotic system but states nothing as to the origin of this peculiar behaviour.  ...  These results are significant for a number of reasons. We note the extremely high sensitivity under variation of the maximal angle ϕ 0 .  ... 
doi:10.1103/physreva.44.2403 pmid:9906222 fatcat:kk44acwsuzdibgywh73exqahxu

Continued fractions with $SL(2, Z)$-branches: combinatorics and entropy

Carlo Carminati, Stefano Isola, Giulio Tiozzo
2018 Transactions of the American Mathematical Society  
We study the dynamics of a family Kα of discontinuous interval maps whose (infinitely many) branches are Möbius transformations in SL(2, Z), and which arise as the critical-line case of the family of (  ...  We provide an explicit construction of the bifurcation locus E KU for this family, showing it is parametrized by Farey words and it has Hausdorff dimension zero.  ...  We also acknowledge the support of the CRM "Ennio de Giorgi" of Pisa and the program "Dynamical Numbers" at the Max Planck Institute of Bonn.  ... 
doi:10.1090/tran/7109 fatcat:apxigbhh5nbtjaxswly6lgra2q
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