Special factors, periodicity, and an application to Sturmian words

2000 ◽  
Vol 36 (12) ◽  
pp. 983-1006 ◽  
Author(s):  
Arturo Carpi ◽  
Aldo de Luca
Keyword(s):  
Sturmian Words ◽  
Special Factors

USEFULNESS OF DIRECTED ACYCLIC SUBWORD GRAPHS IN PROBLEMS RELATED TO STANDARD STURMIAN WORDS

2009 ◽  
Vol 20 (06) ◽  
pp. 1005-1023 ◽  
Author(s):  
PAWEŁ BATURO ◽  
MARCIN PIATKOWSKI ◽  
WOJCIECH RYTTER
Keyword(s):  
Linear Time ◽  
Regular Structure ◽  
Special Structure ◽  
Graph Properties ◽  
Alternative Graph ◽  
Simple Alternative ◽  
Sturmian Words ◽  
Special Factors ◽  
Exponential Size ◽  
Standard Word

The class of finite Sturmian words consists of words having particularly simple compressed representation, which is a generalization of the Fibonacci recurrence for Fibonacci words. The subword graphs of these words (especially their compacted versions) have a very special regular structure. In this paper we investigate this structure in more detail than in previous papers and show how several syntactical properties of Sturmian words follow from their graph properties. Consequently simple alternative graph-based proofs of several known facts are presented. The very special structure of subword graphs leads also to special easy algorithms computing some parameters of Sturmian words: the number of subwords, the critical factorization point, lexicographically maximal suffixes, occurrences of subwords of a fixed length, and right special factors. These algorithms work in linear time with respect to n, the size of the compressed representation of the standard word, though the words themselves can be of exponential size with respect to n. Some of the computed parameters can be also of exponential size, however we provide their linear size compressed representations. We introduce also a new concept related to standard words: Ostrowski automata.

Sturmian words and overexponential codimension growth

2018 ◽  
Vol 95 ◽  
pp. 53-64
Author(s):  
Antonio Giambruno ◽  
Mikhail Zaicev
Keyword(s):  
Sturmian Words

scholarly journals Sturmian words, Lyndon words and trees

1997 ◽  
Vol 178 (1-2) ◽  
pp. 171-203 ◽  
Author(s):  
Jean Berstel ◽  
Aldo de Luca
Keyword(s):  
Sturmian Words ◽  
Lyndon Words

scholarly journals Are Special Processes at Work in the Rapid Intensification of Tropical Cyclones?

2015 ◽  
Vol 143 (3) ◽  
pp. 878-882 ◽  
Author(s):  
Roman Kowch ◽  
Kerry Emanuel
Keyword(s):  
Tropical Cyclone ◽  
Tropical Cyclones ◽  
Internal Variability ◽  
Open Ocean ◽  
Rapid Intensification ◽  
Exponential Distributions ◽  
Frequency Distributions ◽  
Fat Tail ◽  
Dissipation Rates ◽  
Special Factors

Abstract Probably not. Frequency distributions of intensification and dissipation developed from synthetic open-ocean tropical cyclone data show no evidence of significant departures from exponential distributions, though there is some evidence for a fat tail of dissipation rates. This suggests that no special factors govern high intensification rates and that tropical cyclone intensification and dissipation are controlled by statistically random environmental and internal variability.

scholarly journals The Maximal Number of Runs in Standard Sturmian Words

10.37236/2473 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Paweł Baturo ◽  
Marcin Piątkowski ◽  
Wojciech Rytter
Keyword(s):  
Explicit Formula ◽  
Special Class ◽  
Linear Time ◽  
Infinite Sequence ◽  
Integer Sequence ◽  
Sturmian Word ◽  
Compact Representations ◽  
Sturmian Words ◽  
Standard Word

We investigate some repetition problems for a very special class $\mathcal{S}$ of strings called the standard Sturmian words, which  have very compact representations in terms of sequences of integers. Usually the size of this word is exponential with respect to the size of its integer sequence, hence we are dealing with repetition problems in compressed strings. An explicit formula is given for the number $\rho(w)$ of runs in a standard word $w$. We show that $\rho(w)/|w|\le 4/5$ for each $w\in S$, and  there is an infinite sequence of strictly growing words $w_k\in {\mathcal{S}}$ such that $\lim_{k\rightarrow \infty} \frac{\rho(w_k)}{|w_k|} = \frac{4}{5}$. Moreover, we show how to compute the number of runs in a standard Sturmian word in linear time with respect to the size of its compressed representation.

scholarly journals New Potential Solutions for Mentors in the Development of Physical Education Teachers

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
István Győri ◽  
József Márton Pucsok ◽  
Melinda Biró
Keyword(s):  
Higher Education ◽  
Professional Development ◽  
Teacher Education ◽  
Public Education ◽  
Physical Education ◽  
Physical Education Teachers ◽  
The Past ◽  
Key Aspects ◽  
Special Factors

  The Hungarian Educational System, the Higher Education also Teacher Education have been constantly changing over the past decades. According to the results of international and domestic examinations, there is an increasing need for new standards and approaches,  in the entire Public Education, especially Teacher Education sector. The purpose of our study was to examine the key aspects of the mentoring process in physical education. We were trying to identify those special factors and identify new trends in the area of physical education. What is the role of these factors in the process of professional development of a teacher.  

scholarly journals A geometrical approach of palindromic factors of standard billiard words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Jean-Pierre Borel
Keyword(s):  
Geometrical Approach ◽  
International Audience ◽  
Sturmian Words

International audience Many results are already known, concerning the palindromic factors and the palindomic prefixes of Standard billiard words, i.e., Sturmian words and billiard words in any dimension, starting at the origin. We give new geometrical proofs of these results, especially for the existence in any dimension of Standard billiard words with arbitrary long palindromic prefixes.

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