Lyndon Words, the Three Squares Lemma, and Primitive Squares

Hideo Bannai, Takuya Mieno, Yuto Nakashima

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

Abstract

We revisit the so-called “Three Squares Lemma” by Crochemore and Rytter [Algorithmica 1995] and, using arguments based on Lyndon words, derive a more general variant which considers three overlapping squares which do not necessarily share a common prefix. We also give an improved upper bound of on the maximum number of (occurrences of) primitively rooted squares in a string of length n, also using arguments based on Lyndon words. To the best of our knowledge, the only known upper bound was, where is the golden ratio, reported by Fraenkel and Simpson [TCS 1999] obtained via the Three Squares Lemma.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings
EditorsChristina Boucher, Sharma V. Thankachan
PublisherSpringer Science and Business Media Deutschland GmbH
Pages265-273
Number of pages9
ISBN (Print)9783030592110
DOIs
Publication statusPublished - 2020
Event27th International Symposium on String Processing and Information Retrieval, SPIRE 2020 - Orlando, United States
Duration: Oct 13 2020Oct 15 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12303 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference27th International Symposium on String Processing and Information Retrieval, SPIRE 2020
CountryUnited States
CityOrlando
Period10/13/2010/15/20

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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