Here is another small sampling of sequences currently disallowed in the OEIS, roughly in order from slightly likely to become allowed in the future to not likely at all. The decimal representation of this sequence see A is admissible. Since digits 0 to 9 are admissible in the OEIS, one may use a base from 2 to 10, although the default is obviously base The choice of another base needs to be justified e.
Ref: EIS Fig. M 1 Note that sequences of fractions are now allowed as two separate sequences one for the numeratorone for the denominator. Even so, this particular sequence would remain somewhat awkward to include in the OEIS.
D Letters on a Dvorak keyboard. Ref: M. D Operator precedence highest to lowest, grouped in sets of equal precedence in C. Note that the comma is itself an operator, and so is the period. Ref: H. Osborne McGraw-Hillp. Concatenating the subsequences or sets which are disallowed, still leaves the disallowed sequence:.
D Presidents and other historical figures on U.
D Marine Corps ribbons. Very similar to Navy ribbons. Ref: Col. Medals of America Press Both of these were inspired by a similar sequence in the Encyclopedia of Integer Sequencesnamely M However, concatenating the above sequence of subsequences begets the allowed sequence A This is the stable versionapproved on 11 December Jump to: navigationsearch. Category : Disallowed sequences.
Personal tools Log in Request account. Search Advanced search.Results of A set X of integers is k-recognizable if the language of k-ary representations of the elements in X is accepted by a finite automaton.
The celebrated theorem of Cobham from We present several extensions of this result to nonstandard numeration systems, we describe the relationships with substitutive and automatic words and list Cobham-type results in various contexts. In this talk designed for a general audience, I am going to explain these curves that we find all day long in the media and that we want to "flatten". Although I am used to popularizing mathematics, I am not a specialist in applied mathematics, data science nor modeling.
So this talk requires a priori very little mathematical knowledge: a bit of common sense and the manipulation of proportions. The nth term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of n in a suitable numeration system.
In this paper, instead of considering automatic In this paper, instead of considering automatic sequences built on a numeration system with a regular numeration language, we consider these built on languages associated with trees having periodic labeled signatures and, in particular, rational base numeration systems.
We obtain two main characterizations of these sequences. The first one is concerned with r-block substitutions where r morphisms are applied periodically. In particular, we provide examples of such sequences that are not morphic. The second characterization involves the factors, or subtrees of finite height, of the tree associated with the numeration system and decorated by the terms of the sequence.
This work is a contribution to the study of rewrite games. We give sufficient conditions for a game to be such that the losing positions resp.
We formulate several related open questions in parallel with the famous conjecture of Guy about the periodicity of the Grundy function of octal games. Finally we show that more general rewrite games quickly leadt o undecidable problems. The binomial coefficient x,y of the words x and y is the number of times y appears as a scattered subword of x. This concept has received a lot of attention, e.
A few years ago, we introduced the k-binomial equivalence: Two words u and v are k-binomially equivalent if the binomial coefficients u,x and v,x agree for all words x of length up to k. This is a refinement of the usual abelian equivalence. First, I will review several results joint work with P. Salimov, M. Lejeune, J. Leroy, M. Rosenfeld related to k-binomial complexity where factors of length n are counted up to k-binomial equivalence for Sturmian words, Thue-Morse word and Tribonacci word.
Then I will concentrate on k-binomial equivalence classes for finite words. Lejeune, M. Le but de Quand on creuse un peu, on trouve aussi des applications inattendues comme le partage de secrets entre plusieurs intervenants. In general, they appear chaotic, though they exhibit a striking fractal-like pattern. This observation is the first motivation behind this chapter.Skip to main content Skip to table of contents.
Dmitry S. Ananichev, Ilja V. Petrov, Mikhail V. Central Sturmian Words: Recent Developments. Reversible Cellular Automata. Complexity of Quantum Uniform and Nonuniform Automata. On the Membership of Invertible Diagonal Matrices. Revolving-Input Finite Automata. Jean-Pierre Borel, Christophe Reutenauer. A Note on a Result of Daurat and Nivat. Palindromes in Sturmian Words.Carpi A, de Luca A. Harmonic and gold Sturmian words. Quas A, Zamboni L. Periodicity and local complexity.
Plandowski W. Leve F, Seebold P. Conjugation of standard morphisms and a generalization of singular words.
Complexity theory for splicing systems
S Vuillon L. Balanced words. Constant-length substitutions and countable scrambled sets.Find the Sum of the First 30 Terms of the Arithmetic Sequence 3, 7, 11, 15, ...
Harju T, Nowotka D. Periodicity and unbordered words - A proof of Duval's conjecture. The structure of invertible substitutions on a three-letter alphabet.
Klette R, Rosenfeld A. Digital straightness - a review. From monomials to words to graphs. Fiorenzi F. Semi-strongly irreducible shifts. Digital flatness. Tajine M, Daurat A. On local definitions of length of digital curves. About Duval's conjecture. Jenkinson O, Zamboni LQ. Characterisations of balanced words via orderings. Chuan WF.Such sequences are constructed from an infinite product of two substitutions according to a particular Multidimensional Continued Fraction algorithm.
We show that this algorithm is conjugate to a well-known one, the Selmer algorithm. Experimentations Baldwin, suggest that their second Lyapunov exponent is negative which presages finite balance properties.
These words are called Arnoux-Rauzy sequences and are a generalization of Sturmian sequences on a ternary alphabet. It is known that the frequencies of any Arnoux-Rauzy word are well defined and belong to the Rauzy Gasket [ MR ]a fractal set of Lebesgue measure zero. Thus the above condition on the number of special factors is very restrictive for the possible letter frequencies. It is known that these sequences are unbalanced [ MR ]. This article intends to give a positive answer to this question for almost all vectors of letter frequencies with respect to Lebesgue measure.
In recent years, multidimensional continued fraction algorithms were used to obtain ternary balanced sequences with low factor complexity for any given letter frequency vector. In this work, we formalize the algorithm, its matrices, substitutions and associated cocycles and S -adic words.
We also show that the algorithm is conjugate to the Selmer algorithm, a well-known Multidimensional Continued Fraction algorithm. We believe that almost all sequences generated by the algorithm are balanced. Let S be a set of morphisms. The pair sa is called an S -adic representation of w and the sequence s a directive sequence of w. The S -adic representation is said to be primitive whenever the directive sequence s is primitive, i.
Observe that if w has a primitive S -adic representation, then w is uniformly recurrent. It follows that the limit of w n exists. The associated infinite C -adic word is. The following conditions are equivalent. Furthermore, the vector of letter frequencies of 12 and 3 in W x is x. Let us first prove that ii and iii are equivalent.
Therefore the directive sequence s is not primitive. It can be checked that all the matrices of these substitutions have positive entries, so that s is primitive. Let us now assume that iii does not hold. In both cases, the middle entry is unchanged, and the sum of the two other entries decreases by at least y 2.
Finally, let us assume that iii holds and i does not hold. From now on we assume that all entries of F n C x are positive for all n. The sequence of positive integers D m is non-increasing. To reach a contradiction, we need to show that it decreases infinitely often. Similarly, if for large enough m all transitions are of the third type, then iii is not satisfied.
So we must either have infinitely often transitions of the second or fourth type, or infinitely often a transition of the first type followed by a transition of the third type. Let w be a infinite word over some alphabet A. We let Fac w denote the set of factors of wi. We represent it by an array of the form. When the context is clear we omit the information on w and simply write E u. Furthermore, v is a bispecial factor of w 1 and is shorter than u.Equatorial Frequencies.
Archived Week Ending February 14, 18Mar Second week of Feb link downloads: [ Computational and thermodynamic constraints in a molecular design arxiv.
Detailed Derivations arxiv. Part I: Reduction to quadratures arxiv. Randomness for Bilinear Maps arxiv. II: Linnik equidistribution on the supersingular locus arxiv. Segal Spaces: Cartesian Edition arxiv. Archived Week Ending February 7, 24Feb First week of February link downloads [ Odijewicz [ Cabello [ Appraisals on Their Theoretical Relevance arxiv.
Holevo [ Archived Week Ending January 31, 12Feb Final week of January links: [ Luminet [ Fujikawa [ Integrality arxiv. Freedman [ Zyczkowski [Offers end pm EST. Nonexpansive -subdynamics and Nivat's Conjecture. Abstract: For a finite alphabet andthe Morse-Hedlund Theorem states that is periodic if and only if there exists such that the block complexity function satisfiesand this statement is naturally studied by analyzing the dynamics of a -action associated with.
In dimension two, we analyze the subdynamics of a -action associated with and show that if there exist such that the rectangular complexity satisfiesthen the periodicity of is equivalent to a statement about the expansive subspaces of this action. As a corollary, we show that if there exist such thatthen is periodic. This proves a weak form of a conjecture of Nivat in the combinatorics of words. References [Enhancements On Off] What's this? Your device is paired with for another days. Blanchard and A.
MaassDynamical properties of expansive one-sided cellular automataIsrael J. Japan 52no. Brimkov and Reneta P. BarnevaPlane digitization and related combinatorial problemsDiscrete Appl. MR  Julien CassaigneSubword complexity and periodicity in two or more dimensionsDevelopments in language theory Aachen, World Sci.
Fine and H. WilfUniqueness theorems for periodic functionsProc. Pytheas FoggSubstitutions in dynamics, arithmetics and combinatoricsLecture Notes in Mathematics, vol. Edited by V. Ferenczi, C. Mauduit and A. Systems 31no. A-Bno.