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Optimal word chains for the Thue-Morse word
1989
Information and Computation
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We study word chains for the iterates $'(a) of the Thue-Morse word. ...
The length of optimal word chains for #'(a) is proved to be 2n -1, and a conjecture on the enumeration of optimal word chains computing q+'(a) is proposed. 6 ...
The word chain is said to compute a word w if w belongs to the chain. The chain length of w is the smallest length of a word chain computing w. ...
doi:10.1016/0890-5401(89)90056-4
fatcat:spvvj5ncung5dngptzvxozgrxa
Page 2816 of Mathematical Reviews Vol. , Issue 91E
[page]
1991
Mathematical Reviews
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In the case of a one-letter alphabet, word chains correspond to addition chains of natural numbers. ...
The authors investigate word-chain complexity of iterates of the well-known Thue-Morse sequence—an infinite cube-free word over the alphabet {a,b}, which is the basis for constructing square-free words ...
Page 6944 of Mathematical Reviews Vol. , Issue 93m
[page]
1993
Mathematical Reviews
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Packel (1-LFC)
93m:68139 68R15
Bousquet-Mélou, Mireille (F-BORD-LB)
The number of minimal word chains computing the Thue-Morse word. (English summary)
Inform. Process. Lett. 44 (1992), no. 2, 57-64. ...
The infinite word of Thue and Morse is usually defined as the result of infinite iteration of the morphism g(a) =a, 9(b) = b starting from the letter a. ...
Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words
[chapter]
2013
Lecture Notes in Computer Science
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We study the first properties of m-binomial equivalence. We compute the m-binomial complexity of the Sturmian words and of the Thue-Morse word. ...
The binomial coefficient of two words u and v is the number of times v occurs as a subsequence of u. ...
extension of Mahlers theorem on interpolation series, involving binomial coefficients on words. ...
doi:10.1007/978-3-642-40579-2_23
fatcat:hrtnb7uwfjeldjvcsu2hwenlfu
Another generalization of abelian equivalence: Binomial complexity of infinite words
2015
Theoretical Computer Science
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We study the first properties of m-binomial equivalence. We compute the m-binomial complexity of the Sturmian words and of the Thue-Morse word. ...
The binomial coefficient of two words u and v is the number of times v occurs as a subsequence of u. ...
extension of Mahlers theorem on interpolation series, involving binomial coefficients on words. ...
doi:10.1016/j.tcs.2015.07.025
fatcat:7hhgzbqxbndrtlpm7rwotnna7e
The origins of combinatorics on words
2007
European journal of combinatorics (Print)
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These considerations gave rise to early results such as those of Axel Thue at the beginning of the 20th century. ...
We investigate the historical roots of the field of combinatorics on words. They comprise applications and interpretations in algebra, geometry and combinatorial enumeration. ...
The anonymous referee made a great number of concrete suggestions for improvements. ...
doi:10.1016/j.ejc.2005.07.019
fatcat:hgw2rs5ve5g6ral7o3ftmtsney
On the structure of compacted subword graphs of Thue–Morse words and their applications
2012
Journal of Discrete Algorithms
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In particular we show a simple algorithm that checks, for a given string w, if w is a subword of a Thue-Morse word and computes its number of occurrences in nth Thue-Morse word in O(|w| + log n) time and ...
The cdawgs of Thue-Morse words have regular and very simple structure, in particular they oer a powerful (exponential) compression of the set of all subwords in case of nite Thue-Morse words. ...
[3, 11] A word u ∈ Sub(τ ), |u| > 4, is a bispecial factor of the innite Thue-Morse word if and only if ϕ −1 (u) is a (shorter) bispecial word. ...
doi:10.1016/j.jda.2011.01.001
fatcat:zwcdbja6azbulpp3d42pkdb2fe
Streams are Forever
2013
Bulletin of the European Association for Theoretical Computer Science
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In this paper, we describe a number of aspects of streams that we have encountered and studied during the last years. * This research has been funded by the Netherlands Organization for Scientific Research ...
Here one can think of the streams of data queries flowing into search engines, or streams of financial data processed by financial organizations. ...
Now the transformation of the Thue-Morse sequence M to the Toeplitz word T = T 101? ...
dblp:journals/eatcs/EndrullisHK13
fatcat:dpfouwrtwvejfa4ugtivffsgt4
Exploring Predictive States via Cantor Embeddings and Wasserstein Distance
[article]
2022
arXiv
pre-print
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We compute Wasserstein distances between distributions over sequences ("predictions"), using a finite-dimensional embedding of sequences based on the Cantor for the underlying geometry. ...
Recent progress on the self-supervised reconstruction of predictive states from time-series data focused on the use of reproducing kernel Hilbert spaces. ...
The geometric approach is particularly insightful when computing the Wasserstein matrix between predictions estimated from Morse-Thue process data. ...
arXiv:2206.04198v1
fatcat:sexbqqc3gfgp3ar7wcesfv4am4
Quasicrystals, model sets, and automatic sequences
2014
Comptes rendus. Physique
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2014 pre-print arXiv:1401.3725v1 fatcat:re5mbpy6ozhw5jv7auzpiqpam4
We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. ...
Then σ ∞ (0... which is called the Thue-Morse (or Prouhet-Thue-Morse) sequence (see, e.g, [2] for a survey of numerous properties of this sequence).
Theorem 2.4 A model set is a Meyer set. ...
Example 2 The Fibonacci sequence and the Thue-Morse sequence are both morphic (see Example 1, and take B = A and ϕ = id). Furthermore the Thue-Morse sequence is 2-automatic. ...
doi:10.1016/j.crhy.2013.09.002
fatcat:4ttqrigmebbzffitprga5kfdca
Computations for symbolic substitutions
[article]
2017
arXiv
pre-print
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We implement a check to verify that no counterexample exists to the so-called "strong coincidence conjecture" for a large number of substitutions on three and four letters. ...
We study their subshifts (and related spaces) with an emphasis on examples of computations. ...
This research used the SPECTRE High Performance Computing Facility at the University of Leicester. ...
arXiv:1705.11130v1
fatcat:ifrgdsibv5ad3dk4miepkxroni
Gaps in the Thue–Morse word
[article]
2021
arXiv
pre-print
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We give an explicit method to compute the discrepancy of the number of occurrences of the block 01 in the Thue–Morse sequence. ...
The Thue–Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. ...
Finally, we thank Michel Rigo for fruitful discussions on the topic and Clemens Müllner for pointing out that the case of arbitrary factors can be reduced to the case 01. ...
arXiv:2102.01018v2
fatcat:sdsm7fnmdvhkbc75ewtfugxauu
Substitutions and their generalisations
[article]
2023
arXiv
pre-print
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We also present a planar example (which is a two-dimensional generalisation of the Thue--Morse substitution), whose diffraction is purely singular continuous. ...
properties which make them viable models of materials with almost periodic order. ...
Acknowledgements The author would like to explicitly mention that the methods, results, and examples presented in Sections 4 and 5 of this review are based on a series of joint works with Dan Rust (Milton ...
arXiv:2311.05731v1
fatcat:ujmtieyacfhffaqqo3lxbklvb4
Automata and automatic sequences
[article]
2022
arXiv
pre-print
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Needless to say, we feel that the order we propose is the most natural one. References appear at the end of each one of the parts which implies some redundancy. ...
Extra references are listed at the very end of our paper. ...
We shall apply these results to the Ising chain in Part VII. ...
arXiv:2212.08857v1
fatcat:6tzbo6wuubc7rogtemgzj2nwda
Exact Regularity and the Cohomology of Tiling Spaces
[article]
2018
arXiv
pre-print
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If Ȟ^d(Ω_T, Q) = Q^k, then there exist k patches whose appearance govern the number of appearances of every other patch. ...
If T is also one-dimensional, we put constraints on the measure of any cylinder set in Ω_T. ...
I also thank Bill Kalahurka for figures of the equithirds tiling, and the anonymous referee for pointing out an error in an earlier version of Theorem 3. ...
arXiv:1004.2281v2
fatcat:4ktc5yehyfhyrkqfsppddfpleq
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