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On the Number of Distinct Squares in Finite Sequences: Some Old and New Results

  • Srečko Brlek
  • , Shuo Li*
  • *Corresponding author for this work
  • Université du Québec à Montréal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A square is a word of the form uu, where u is a finite word. The problem of determining the number of distinct squares in a finite word was initially explored by Fraenkel and Simpson in 1998. They proved that the number of distinct squares, denoted as Sq (w), in a finite word w of length n is upper bounded by 2n and conjectured that Sq (w) is no larger than n. In this note, we review some old and new findings concerning the square-counting problem and prove that Sq (w) ≤ n- Θ(log 2(n) ).

Original languageEnglish
Title of host publicationCombinatorics on Words - 14th International Conference, WORDS 2023, Proceedings
EditorsAnna Frid, Robert Mercaş
PublisherSpringer Science and Business Media Deutschland GmbH
Pages35-44
Number of pages10
ISBN (Print)9783031331794
DOIs
StatePublished - 2023
Externally publishedYes
Event14th International Conference on Combinatorics on Words, WORDS 2023 - Umeå, Sweden
Duration: 12 Jun 202316 Jun 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13899 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Conference on Combinatorics on Words, WORDS 2023
Country/TerritorySweden
CityUmeå
Period12/06/2316/06/23

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