On morphisms generating run-rich strings

Kazuhiko Kusano, Kazuyuki Narisawa, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

A run in a string is a periodic substring which is extendable neither to the left nor to the right with the same period. Strings containing many runs are of interest. In this paper, we focus on the series of strings {Ψ(Φ(a))}i≥0 generated by two kinds of morphisms, Φ: {a,b, c} → {a,b, c}* and Ψ: {a,b, c} → {0,1}*. We reveal a simple morphism Φr plays a critical role to generate run-rich strings. Combined with a morphism Ψ′, the strings {Ψ′(4(a))}i≥0 achieves exactly the same lower bound as the current best lower bound for the maximum number ρ(n) of runs in a string of length n. Moreover, combined with another morphism Ψ′′, the strings {Ψ′′(Φir(a))};≥o give a new lower bound for the maximum value σ(n) of the sum of exponents of runs in a string of length n.

Original languageEnglish
Title of host publicationProceedings of the Prague Stringology Conference 2013, PSC 2013
Pages35-47
Number of pages13
Publication statusPublished - 2013 Oct 1
EventPrague Stringology Conference 2013, PSC 2013 - Prague, Czech Republic
Duration: 2013 Sep 22013 Sep 4

Publication series

NameProceedings of the Prague Stringology Conference 2013, PSC 2013

Other

OtherPrague Stringology Conference 2013, PSC 2013
CountryCzech Republic
CityPrague
Period13/9/213/9/4

Keywords

  • Morphic word
  • Repetition
  • Run
  • Sum of exponents

ASJC Scopus subject areas

  • Mathematics(all)

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