Logo image
The new periodicity lemma revisited
Journal article   Open access   Peer reviewed

The new periodicity lemma revisited

H. Bai, F. Franěk and W.F. Smyth
Discrete Applied Mathematics, Vol.212, pp.30-36
2016
pdf
DA4146R1.pdfDownloadView
Author’s Version Open Access
url
Link to Published Version *Subscription may be requiredView

Abstract

In 2006, the New Periodicity Lemma (NPL) was published, showing that the occurrence of two squares starting at a position ii in a string necessarily precludes the occurrence of other squares of specified period in a specified neighbourhood of ii. The proof of this lemma was complex, breaking down into 14 subcases, and requiring that the shorter of the two squares be regular. In this paper we significantly relax the conditions required by the NPL and removing the need for regularity altogether, and we establish a more precise result using a simpler proof based on lemmas that expose new combinatorial structures in a string, in particular a canonical factorization for any two squares that start at the same position.

Details

Metrics

77 File views/ downloads
67 Record Views

InCites Highlights

These are selected metrics from InCites Benchmarking & Analytics tool, related to this output

Collaboration types
Domestic collaboration
International collaboration
Citation topics
4 Electrical Engineering, Electronics & Computer Science
4.182 Data Structures, Algorithms & Complexity
4.182.1103 Efficient Algorithms
Web Of Science research areas
Mathematics, Applied
ESI research areas
Engineering
Logo image