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

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. ...

##
###
On extremal properties of the Fibonacci word

2008
*
RAIRO - Theoretical Informatics and Applications
*

We survey several quantitative problems on infinite

doi:10.1051/ita:2008003
fatcat:kzykr3odoncyzk2pyvqp6ip3ie
*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 ...##
###
Strong Repetitions in Sturmian Strings
[article]

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*. ...

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

2018
*
arXiv
*
pre-print

For example, an unusually large limit for

arXiv:1811.05777v1
fatcat:olbl25c62fadtnyyh5773mwbce
*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. ...##
###
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) ...

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

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. ...

##
###
COMBINATORICS ON WORDS – A TUTORIAL
[chapter]

2004
*
Current Trends in Theoretical Computer Science
*

Shallit for their careful reading

doi:10.1142/9789812562494_0059
fatcat:rb3muz6tsffbrpm26j4aj2rkey
*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 ...##
###
New types of solvability in PT symmetric quantum theory

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. ...

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

2020
*
arXiv
*
pre-print

This approach allows us to establish uniformity

arXiv:2006.15348v1
fatcat:7wmm667soba2fjpohrdvb337vm
*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. ...##
###
Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081)

2011
*
Dagstuhl Reports
*

Scientists working

doi:10.4230/dagrep.1.2.47
dblp:journals/dagstuhl-reports/CrochemoreKMN11
fatcat:s3v55bqr4fbdfo5kztirfoljqm
*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. ...##
###
Breaking Time Reversal Symmetry in Chaotic Driven Rydberg Atoms

2000
*
Annals of Physics
*

mixes

doi:10.1006/aphy.2000.6051
fatcat:oqux5qx74nebvkjs7vri3vcpca
*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] ...##
###
Spectral triples for subshifts
[article]

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). ...

##
###
Subject index volumes 101–150

1995
*
Theoretical Computer Science
*

mentioned

doi:10.1016/0304-3975(95)90001-2
fatcat:omihw2cp6vb2hgwdfiksnt4ftu
*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 ...##
###
Quantum chaos and analytic structure of the spectrum

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 . ...

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

2018
*
Transactions of the American Mathematical Society
*

We study

doi:10.1090/tran/7109
fatcat:apxigbhh5nbtjaxswly6lgra2q
*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. ...
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