Square-Free Partial Words with Many Wildcards

2018 ◽  
Vol 29 (05) ◽  
pp. 845-860
Author(s):  
Daniil Gasnikov ◽  
Arseny M. Shur
Keyword(s):  
Natural Generalization ◽  
Interesting Phenomenon ◽  
Maximal Density ◽  
Classical Notion ◽  
Partial Word ◽  
Partial Words ◽  
Free Word

We contribute to the study of square-free words. The classical notion of a square-free word has a natural generalization to partial words, studied in several papers since 2008. We prove that the maximal density of wildcards in the ternary infinite square-free partial word is surprisingly big: [Formula: see text]. Further we show that the density of wildcards in a finitary infinite square-free partial words is at most [Formula: see text] and this bound is reached by a quaternary word. We demonstrate that partial square-free words can be viewed as “usual” square-free words with some letters replaced by wildcards and introduce the corresponding characteristic of infinite square-free words, called flexibility. The flexibility is estimated for some important words and classes of words; an interesting phenomenon is the existence of “rigid” square-free words, having no room for wildcards at all.

CYCLIC PARTIAL WORDS

2020 ◽  
Vol 9 (11) ◽  
pp. 9219-9230
Author(s):  
R.K. Kumari ◽  
R. Arulprakasam ◽  
R. Perumal ◽  
V.R. Dare
Keyword(s):  
Dna Sequencing ◽  
Partial Word ◽  
Partial Words ◽  
Cyclic Words

Partial words are linear words with holes. Cyclic words are derived from linear words by linking its first letter after the last one. Both partial words and cyclic words have wide applications in DNA sequencing. In this paper we introduce cyclic partial words and discuss their periodicity and certain properties. We also establish representation of a cyclic partial word using trees.

scholarly journals Counting Bordered Partial Words by Critical Positions

10.37236/625 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Emily Allen ◽  
F. Blanchet-Sadri ◽  
Cameron Byrum ◽  
Mihai Cucuringu ◽  
Robert Mercaş
Keyword(s):  
Combinatorial Property ◽  
Finite Alphabet ◽  
Theoretical Problem ◽  
Fixed Size ◽  
Fixed Length ◽  
Word Sequence ◽  
Partial Word ◽  
Recursive Formulas ◽  
Partial Words

A partial word, sequence over a finite alphabet that may have some undefined positions or holes, is bordered if one of its proper prefixes is compatible with one of its suffixes. The number theoretical problem of enumerating all bordered full words (the ones without holes) of a fixed length $n$ over an alphabet of a fixed size $k$ is well known. It turns out that all borders of a full word are simple, and so every bordered full word has a unique minimal border no longer than half its length. Counting bordered partial words having $h$ holes with the parameters $k, n$ is made extremely more difficult by the failure of that combinatorial property since there is now the possibility of a minimal border that is nonsimple. Here, we give recursive formulas based on our approach of the so-called simple and nonsimple critical positions.

ALGORITHMIC COMBINATORICS ON PARTIAL WORDS

2012 ◽  
Vol 23 (06) ◽  
pp. 1189-1206 ◽  
Author(s):  
F. BLANCHET-SADRI
Keyword(s):  
Molecular Biology ◽  
Data Compression ◽  
Pattern Avoidance ◽  
Finite Alphabet ◽  
Open Problems ◽  
The Past ◽  
Partial Word ◽  
De Bruijn ◽  
Subword Complexity ◽  
Partial Words

Algorithmic combinatorics on partial words, or sequences of symbols over a finite alphabet that may have some do-not-know symbols or holes, has been developing in the past few years. Applications can be found, for instance, in molecular biology for the sequencing and analysis of DNA, in bio-inspired computing where partial words have been considered for identifying good encodings for DNA computations, and in data compression. In this paper, we focus on two areas of algorithmic combinatorics on partial words, namely, pattern avoidance and subword complexity. We discuss recent contributions as well as a number of open problems. In relation to pattern avoidance, we classify all binary patterns with respect to partial word avoidability, we classify all unary patterns with respect to hole sparsity, and we discuss avoiding abelian powers in partial words. In relation to subword complexity, we generate and count minimal Sturmian partial words, we construct de Bruijn partial words, and we construct partial words with subword complexities not achievable by full words (those without holes).

FINE AND WILF'S THEOREM FOR PARTIAL WORDS WITH ARBITRARILY MANY WEAK PERIODS

2010 ◽  
Vol 21 (05) ◽  
pp. 705-722 ◽  
Author(s):  
F. BLANCHET-SADRI ◽  
TAKTIN OEY ◽  
TIMOTHY D. RANKIN
Keyword(s):  
Arbitrary Number ◽  
Finite Sequences ◽  
Partial Word ◽  
Partial Words

Fine and Wilf's well-known theorem states that any word having periods p,q and length at least p+q- gcd (p,q) also has gcd (p,q) as a period. Moreover, the length p+q- gcd (p,q) is critical since counterexamples can be provided for shorter words. This result has since been extended to partial words, or finite sequences that may contain some "holes." More precisely, any partial word u with H holes having weak periods p,q and length at least the so-denoted lH(p,q) also has strong period gcd (p,q) provided u is not (H,(p,q))-special. This extension was done for one hole by Berstel and Boasson (where the class of (1,(p,q))-special partial words is empty), and for an arbitrary number of holes by Blanchet-Sadri. In this paper, we further extend these results, allowing an arbitrary number of weak periods. In addition to speciality, the concepts of intractable period sets and interference between periods play a role.

“Little Trio” for clarinet, bassoon and piano

2018 ◽  
pp. 75-79
Author(s):  
N. Yakovchuk
Keyword(s):  
Chamber Music ◽  
Instrumental Music ◽  
Instrumental Ensemble ◽  
Interesting Phenomenon ◽  
Theoretical Understanding ◽  
Classical Traditions ◽  
And Performance ◽  
Instrumental Ensembles ◽  
Written Compositions ◽  
First Time

The chamber-instrumental ensemble music in the Ukrainian musical culture of the last third of the 20th and the beginning of the 21st centuries occupies one of the leading places and is characterized by powerful processes in its development. Such circumstances caused the Ukrainian musicologist interests to the problems of chamber-instrumental music creativity and performance. There are appeared researches in the field of theory, history and performance problems covering the most important questions like chamber music definitions, specific genre issues, the growing function of piano in the Ukrainian chamber music, the increasing questions of technique and timbre importance of modern instrumental ensembles. In the significant multifaceted creative work of contemporary Ukrainian composer, Oleksandr Yakovchuk, the genre of chamber instrumental ensemble music represents a complex and interesting phenomenon. Original and skillfully written compositions reflect artistic world of the composer of postmodern time and gained recognition in music life of Ukraine and beyond. These works are highly appreciated in performing practice of our days. The purpose of the article is to analyze the work — “Little Trio” for clarinet, bassoon and piano (1980), which has the signs of neoclassical tendency in the composer’s style. The methodological basis of this research is a comprehensive approach in theoretical understanding of the subject of research (the methods of textology, source study as well as the method of interviewing the author were used). The scientific novelty of this article is in the priority of its main provisions, since the “Little Trio” entered the scientific circulation for the first time. The three-movement “Little Trio” (1980) is notable for the light feeling of timbre colours and the shape clarity. The Ist movement — Allegretto giocoso — is written in a sonata form following all classical traditions. Quite interesting are the two monologues of clarinet and bassoon from the IInd movement, they represent very modern line in Ukrainian chamber music — the possibility of sincere confession which comes through the solo cadence. In the IIIrd movement, the composer took advantage from the folk Ukrainian dance “hopak” using the rhythm of it and creating dance character of the Final.

On mappings with finite length distortion on Riemann surfaces

2019 ◽  
Vol 33 ◽  
Author(s):  
Serhii Volkov ◽  
Vladimir Ryazanov
Keyword(s):  
Finite Length ◽  
Riemann Surfaces ◽  
Boundary Behavior ◽  
Main Tool ◽  
Natural Generalization ◽  
Finite Distortion ◽  
Lipschitz Mappings ◽  
Geometric Function ◽  
Mappings With Finite Distortion ◽  
Length Distortion

The present paper is a natural continuation of our previous paper (2017) on the boundary behavior of mappings in the Sobolev classes on Riemann surfaces, where the reader will be able to find the corresponding historic comments and a discussion of many definitions and relevant results. The given paper was devoted to the theory of the boundary behavior of mappings with finite distortion by Iwaniec on Riemannian surfaces first introduced for the plane in the paper of Iwaniec T. and Sverak V. (1993) On mappings with integrable dilatation and then extended to the spatial case in the monograph of Iwaniec T. and Martin G. (2001) devoted to Geometric function theory and non-linear analysis. At the present paper, it is developed the theory of the boundary behavior of the so--called mappings with finite length distortion first introduced in the paper of Martio O., Ryazanov V., Srebro U. and Yakubov~E. (2004) in the spatial case, see also Chapter 8 in their monograph (2009) on Moduli in modern mapping theory. As it was shown in the paper of Kovtonyuk D., Petkov I. and Ryazanov V. (2017) On the boundary behavior of mappings with finite distortion in the plane, such mappings, generally speaking, are not mappings with finite distortion by Iwaniec because their first partial derivatives can be not locally integrable. At the same time, this class is a generalization of the known class of mappings with bounded distortion by Martio--Vaisala from their paper (1988). Moreover, this class contains as a subclass the so-called finitely bi-Lipschitz mappings introduced for the spatial case in the paper of Kovtonyuk D. and Ryazanov V. (2011) On the boundary behavior of generalized quasi-isometries, that in turn are a natural generalization of the well-known classes of bi-Lipschitz mappings as well as isometries and quasi-isometries. In the research of the local and boundary behavior of mappings with finite length distortion in the spatial case, the key fact was that they satisfy some modulus inequalities which was a motivation for the consideration more wide classes of mappings, in particular, the Q-homeomorphisms (2005) and the mappings with finite area distortion (2008). Hence it is natural that under the research of mappings with finite length distortion on Riemann surfaces we start from establishing the corresponding modulus inequalities that are the main tool for us. On this basis, we prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extension to the boundary of the mappings with finite length distortion between domains on arbitrary Riemann surfaces.

Quality of Life (QOL) of Balinese Women Working in Spa Tourism Industry

2015 ◽  
Vol 1 (1) ◽  
pp. 13
Author(s):  
Putu Sucita Yanthy ◽  
Luh Gede Leli Kusuma Dewi ◽  
W. Citra Juwitasari
Keyword(s):  
Quality Of Life ◽  
Tourism Industry ◽  
Family Needs ◽  
Interesting Phenomenon ◽  
Tourist Destinations ◽  
Foreign Countries ◽  
The Family ◽  
Two Factors ◽  
Material Factor

Bali is one of spa tourist destinations having various categories of spas and spa treatments, and the most important is the spa therapists. Spa development becomes an interesting phenomenon to be studied when it is associated with an involvement of Balinese women as spa therapists in foreign countries. The world’s demand for Balinese spa therapists has become the motivation of women to work in this area. The work and life of Balinese spa therapists while they are working in foreign countries serve as parameters to know their quality of life, and these parameters are also the main focus of this study. Through in-depth interviews and questionnaires distributed to 20 therapists it was found out that 85 percent of them have revealed an improvement in their quality of life that is influenced by two factors: the material and intimacy factors. The material factor in question refers to the economic improvement of the family as they could earn enough income to cover their family needs. The intimacy factor in question refers to closeness and a sense of solidarity fostered while they are working abroad and the relationship within the family. This study concludes that the most important part of the development of spa in Bali is its female Balinese spa therapists due to the image that Balinese women working as spa therapists are loyal, hard-working and honest making them in demand among tourists who are seeking spa treatments. Being a spa therapist can improve their quality of life, which means that subjectively both material and intimacy factors are the aspects that affect the quality of life of the Balinese spa therapists.

Pragmatics for Latin

2019 ◽  
Author(s):  
A. M. Devine ◽  
Laurence D. Stephens
Keyword(s):  
Noun Phrase ◽  
Word Order ◽  
Information Structure ◽  
Descriptive Analysis ◽  
Informational Content ◽  
Compositional Process ◽  
Association With Focus ◽  
Narrow Scope ◽  
Order Language ◽  
Free Word

Latin is often described as a free word order language, but in general each word order encodes a particular information structure: in that sense, each word order has a different meaning. This book provides a descriptive analysis of Latin information structure based on detailed philological evidence and elaborates a syntax-pragmatics interface that formalizes the informational content of the various different word orders. The book covers a wide ranges of issues including broad scope focus, narrow scope focus, double focus, topicalization, tails, focus alternates, association with focus, scrambling, informational structure inside the noun phrase and hyperbaton (discontinuous constituency). Using a slightly adjusted version of the structured meanings theory, the book shows how the pragmatic meanings matching the different word orders arise naturally and spontaneously out of the compositional process as an integral part of a single semantic derivation covering denotational and informational meaning at one and the same time.

A Relative Notion of Natural Generalization

1975 ◽  
Vol 42 (1) ◽  
pp. 46-48 ◽  
Author(s):  
Nathan Stemmer
Keyword(s):  
Natural Generalization ◽  
Relative Notion
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