• Corpus ID: 6661557

Combinatorics of the Interrupted Period

@inproceedings{Thierry2015CombinatoricsOT,
  title={Combinatorics of the Interrupted Period},
  author={Adrien Thierry},
  booktitle={Stringology},
  year={2015}
}
  • A. Thierry
  • Published in Stringology 1 May 2014
  • Mathematics
This article is about discrete periodicities and their combinatorial structure. It describes the unique structure caused by the alteration of a pattern in a repetition. That alteration of a pattern could be "heard" as the disturbance that one can hear when a record is scratched and jumps. 

The New Periodicity Lemma revisited

Novel Structural Properties and An Improved Bound for the Number Distinct Squares in a Strings

Combinatorics on words explore words – often called strings in the computer science community, or monoids in mathematics – and their structural properties. One of the most studied question deals with

A proof that a word of length n has less than 1.5n distinct squares.

We are interested in the maximal number of distinct squares in a word. This problem was introduced by Fraenkel and Simpson, who presented a bound of 2n for a word of length n, and conjectured that

STRUCTURAL FACTORIZATION OF SQUARES IN STRINGS

A balanced double square in a string x consists of two squares starting in the same position and of comparable lengths. We present a unique factorization of the longer square into primitive

References

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The New Periodicity Lemma revisited

On a lemma of Crochemore and Rytter

Squares, cubes, and time-space efficient string searching

A cleaner version and a simpler analysis of the GS algorithm that corrects the algorithm given in [GS2] for the computation of periods and presents an optimal parallel algorithm for pattern preprocessing.

How Many Squares Can a String Contain?

No position in any word can be the beginning of the rightmost occurrence of more than two squares, from which the maximum number of distinct primitive rooted squares in a word of length n is deduced.

Computing Patterns in Strings

A basic general introduction to the algorithms (methods) that efficiently compute patterns in strings, which is fundamental to many fields molecular biology, cryptography, data compression, computer vision, speech recognition, computational geometry, and many others.

Adrien Thierry: Combinatorics of the Interrupted Period

  • Adrien Thierry: Combinatorics of the Interrupted Period

Ilie : A simple proof that a word of length n has at most 2 n distinct squares