TY - GEN

T1 - On morphisms generating run-rich strings

AU - Kusano, Kazuhiko

AU - Narisawa, Kazuyuki

AU - Shinohara, Ayumi

PY - 2013/10/1

Y1 - 2013/10/1

N2 - 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.

AB - 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.

KW - Morphic word

KW - Repetition

KW - Run

KW - Sum of exponents

UR - http://www.scopus.com/inward/record.url?scp=84884614262&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884614262&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84884614262

SN - 9788001053300

T3 - Proceedings of the Prague Stringology Conference 2013, PSC 2013

SP - 35

EP - 47

BT - Proceedings of the Prague Stringology Conference 2013, PSC 2013

T2 - Prague Stringology Conference 2013, PSC 2013

Y2 - 2 September 2013 through 4 September 2013

ER -