scholarly journals Quasi-Sturmian colorings on regular trees

2019 ◽  
Vol 40 (12) ◽  
pp. 3403-3419
Author(s):  
DONG HAN KIM ◽  
SEUL BEE LEE ◽  
SEONHEE LIM ◽  
DEOKWON SIM
Keyword(s):  
Infinite Words ◽  
Different Types ◽  
Sturmian Words

Quasi-Sturmian words, which are infinite words with factor complexity eventually $n+c$ share many properties with Sturmian words. In this article, we study the quasi-Sturmian colorings on regular trees. There are two different types, bounded and unbounded, of quasi-Sturmian colorings. We obtain an induction algorithm similar to Sturmian colorings. We distinguish them by the recurrence function.

scholarly journals RECENT RESULTS ON EXTENSIONS OF STURMIAN WORDS

2002 ◽  
Vol 12 (01n02) ◽  
pp. 371-385 ◽  
Author(s):  
JEAN BERSTEL
Keyword(s):  
Infinite Words ◽  
Combinatorial Properties ◽  
The Past ◽  
Letter Alphabet ◽  
Sturmian Words

Sturmian words are infinite words over a two-letter alphabet that admit a great number of equivalent definitions. Most of them have been given in the past ten years. Among several extensions of Sturmian words to larger alphabets, the Arnoux–Rauzy words appear to share many of the properties of Sturmian words. In this survey, combinatorial properties of these two families are considered and compared.

scholarly journals Rigidity and Substitutive Dendric Words

2018 ◽  
Vol 29 (05) ◽  
pp. 705-720 ◽  
Author(s):  
V. Berthé ◽  
F. Dolce ◽  
F. Durand ◽  
J. Leroy ◽  
D. Perrin
Keyword(s):  
Bipartite Graphs ◽  
Constant Length ◽  
Infinite Words ◽  
Algebraic Properties ◽  
Interval Exchanges ◽  
Left And Right ◽  
Sturmian Words

Dendric words are infinite words that are defined in terms of extension graphs. These are bipartite graphs that describe the left and right extensions of factors. Dendric words are such that all their extension graphs are trees. They are also called tree words. This class of words includes classical families of words such as Sturmian words, codings of interval exchanges, or else, Arnoux–Rauzy words. We investigate here the properties of substitutive dendric words and prove some rigidity properties, that is, algebraic properties on the set of substitutions that fix a dendric word. We also prove that aperiodic minimal dendric subshifts (generated by dendric words) cannot have rational topological eigenvalues, and thus, cannot be generated by constant length substitutions.

ON THE PALINDROMIC COMPLEXITY OF INFINITE WORDS

2004 ◽  
Vol 15 (02) ◽  
pp. 293-306 ◽  
Author(s):  
S. BRLEK ◽  
S. HAMEL ◽  
M. NIVAT ◽  
C. REUTENAUER
Keyword(s):  
Mild Condition ◽  
Infinite Words ◽  
Finite Set ◽  
Sturmian Words ◽  
Check Condition

We study the problem of constructing infinite words having a prescribed finite set P of palindromes. We first establish that the language of all words with palindromic factors in P is rational. As a consequence we derive that there exists, with some additional mild condition, infinite words having P as palindromic factors. We prove that there exist periodic words having the maximum number of palindromes as in the case of Sturmian words, by providing a simple and easy to check condition. Asymmetric words, those that are not the product of two palindromes, play a fundamental role and an enumeration is provided.

scholarly journals AVOIDING ABELIAN POWERS IN BINARY WORDS WITH BOUNDED ABELIAN COMPLEXITY

2011 ◽  
Vol 22 (04) ◽  
pp. 905-920 ◽  
Author(s):  
JULIEN CASSAIGNE ◽  
GWÉNAËL RICHOMME ◽  
KALLE SAARI ◽  
LUCA Q. ZAMBONI
Keyword(s):  
Infinite Number ◽  
Open Problem ◽  
Orbit Closure ◽  
Infinite Words ◽  
Morphic Image ◽  
In The Beginning ◽  
Sturmian Words ◽  
Free Word ◽  
Recurrent Word

The notion of Abelian complexity of infinite words was recently used by the three last authors to investigate various Abelian properties of words. In particular, using van der Waerden's theorem, they proved that if a word avoids Abelian k-powers for some integer k, then its Abelian complexity is unbounded. This suggests the following question: How frequently do Abelian k-powers occur in a word having bounded Abelian complexity? In particular, does every uniformly recurrent word having bounded Abelian complexity begin in an Abelian k-power? While this is true for various classes of uniformly recurrent words, including for example the class of all Sturmian words, in this paper we show the existence of uniformly recurrent binary words, having bounded Abelian complexity, which admit an infinite number of suffixes which do not begin in an Abelian square. We also show that the shift orbit closure of any infinite binary overlap-free word contains a word which avoids Abelian cubes in the beginning. We also consider the effect of morphisms on Abelian complexity and show that the morphic image of a word having bounded Abelian complexity has bounded Abelian complexity. Finally, we give an open problem on avoidability of Abelian squares in infinite binary words and show that it is equivalent to a well-known open problem of Pirillo–Varricchio and Halbeisen–Hungerbühler.

scholarly journals On the number of factors in codings of three interval exchange

2011 ◽  
Vol Vol. 13 no. 3 (Graph Theory) ◽  
Author(s):  
Petr Ambrož ◽  
Anna Frid ◽  
Zuzana Masáková ◽  
Edita Pelantová
Keyword(s):  
Graph Theory ◽  
Asymptotic Formula ◽  
Interval Exchange ◽  
Infinite Words ◽  
Number Of Factors ◽  
Strong Relation ◽  
International Audience ◽  
Sturmian Words

Graph Theory International audience We consider exchange of three intervals with permutation (3, 2, 1). The aim of this paper is to count the cardinality of the set 3iet (N) of all words of length N which appear as factors in infinite words coding such transformations. We use the strong relation of 3iet words and words coding exchange of two intervals, i.e., Sturmian words. The known asymptotic formula #2iet(N)/N-3 similar to 1/pi(2) for the number of Sturmian factors allows us to find bounds 1/3 pi(2) +o(1) \textless= #3iet(N)N-4 \textless= 2 pi(2) + o(1)

scholarly journals Words with many Palindrome Pair Factors

10.37236/5583 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Adam Borchert ◽  
Narad Rampersad
Keyword(s):  
Infinite Words ◽  
Sturmian Word ◽  
Proper Factor ◽  
Sturmian Words

Motivated by a conjecture of Frid, Puzynina, and Zamboni, we investigate infinite words with the property that for infinitely many $n$, every length-$n$ factor is a product of two palindromes. We show that every Sturmian word has this property, but this does not characterize the class of Sturmian words. We also show that the Thue—Morse word does not have this property. We investigate finite words with the maximal number of distinct palindrome pair factors and characterize the binary words that are not palindrome pairs but have the property that every proper factor is a palindrome pair.

EPISTURMIAN WORDS: SHIFTS, MORPHISMS AND NUMERATION SYSTEMS

2004 ◽  
Vol 15 (02) ◽  
pp. 329-348 ◽  
Author(s):  
JACQUES JUSTIN ◽  
GIUSEPPE PIRILLO
Keyword(s):  
Finite Alphabet ◽  
Infinite Words ◽  
Complete Answer ◽  
Matrix Formula ◽  
Numeration Systems ◽  
Sturmian Words ◽  
Insight Into

Episturmian words, which include the Arnoux-Rauzy sequences, are infinite words on a finite alphabet generalizing the Sturmian words and sharing many of their same properties. This was studied in previous papers. Here we gain a deeper insight into these properties. This leads in particular to consider numerations systems similar to the Ostrowski ones and to give a matrix formula for computing the number of representations of an integer in such a system. We also obtain a complete answer to the question: if an episturmian word is morphic, which shifts of it, if any, also are morphic ?

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Differentiating between different forms of moral obligations

2020 ◽  
Vol 43 ◽  
Author(s):  
Rajen A. Anderson ◽  
Benjamin C. Ruisch ◽  
David A. Pizarro
Keyword(s):  
Moral Character ◽  
Moral Obligations ◽  
Different Types

Abstract We argue that Tomasello's account overlooks important psychological distinctions between how humans judge different types of moral obligations, such as prescriptive obligations (i.e., what one should do) and proscriptive obligations (i.e., what one should not do). Specifically, evaluating these different types of obligations rests on different psychological inputs and has distinct downstream consequences for judgments of moral character.

Ultrastructural Investigations of the Contractile Filaments of Amoebae

1974 ◽  
Vol 32 ◽  
pp. 188-189
Author(s):  
P.L. Moore
Keyword(s):  
Cytoplasmic Streaming ◽  
Three Dimensional ◽  
Freeze Fracture ◽  
Amoeboid Movement ◽  
Different Types ◽  
Chemical Conditions ◽  
Complete Interpretation

Previous freeze fracture results on the intact giant, amoeba Chaos carolinensis indicated the presence of a fibrillar arrangement of filaments within the cytoplasm. A complete interpretation of the three dimensional ultrastructure of these structures, and their possible role in amoeboid movement was not possible, since comparable results could not be obtained with conventional fixation of intact amoebae. Progress in interpreting the freeze fracture images of amoebae required a more thorough understanding of the different types of filaments present in amoebae, and of the ways in which they could be organized while remaining functional.The recent development of a calcium sensitive, demembranated, amoeboid model of Chaos carolinensis has made it possible to achieve a better understanding of such functional arrangements of amoeboid filaments. In these models the motility of demembranated cytoplasm can be controlled in vitro, and the chemical conditions necessary for contractility, and cytoplasmic streaming can be investigated. It is clear from these studies that “fibrils” exist in amoeboid models, and that they are capable of contracting along their length under conditions similar to those which cause contraction in vertebrate muscles.

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