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Avoiding Three Consecutive Blocks of the Same Size and Same Sum

Authors:

Julien Cassaigne,

James D. Currie,

Luke Schaeffer,

Jeffrey ShallitAuthors Info & Claims

Journal of the ACM (JACM), Volume 61, Issue 2

Article No.: 10, Pages 1 - 17

https://doi.org/10.1145/2590775

Published: 24 April 2014 Publication History

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Abstract

We show that there exists an infinite word over the alphabet {0, 1, 3, 4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from 1994.

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Fici GPuzynina S(2023)Abelian combinatorics on words: A surveyComputer Science Review10.1016/j.cosrev.2022.10053247(100532)Online publication date: Feb-2023
https://doi.org/10.1016/j.cosrev.2022.100532
Mandache M(2022)Finding Certain Arithmetic Progressions in 2-Coloured Cyclic GroupsCombinatorica10.1007/s00493-022-4901-x42:Suppl 2(1385-1408)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s00493-022-4901-x
Lejeune MRigo MRosenfeld M(2020)Templates for the k-binomial complexity of the Tribonacci wordAdvances in Applied Mathematics10.1016/j.aam.2019.101947112(101947)Online publication date: Jan-2020
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Index Terms

Avoiding Three Consecutive Blocks of the Same Size and Same Sum
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation
  1. Formal languages and automata theory

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Published In

Journal of the ACM Volume 61, Issue 2

April 2014

206 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2605175

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 24 April 2014

Accepted: 01 November 2013

Revised: 01 July 2013

Received: 01 September 2011

Published in JACM Volume 61, Issue 2

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Fici GPuzynina S(2023)Abelian combinatorics on words: A surveyComputer Science Review10.1016/j.cosrev.2022.10053247(100532)Online publication date: Feb-2023
https://doi.org/10.1016/j.cosrev.2022.100532
Mandache M(2022)Finding Certain Arithmetic Progressions in 2-Coloured Cyclic GroupsCombinatorica10.1007/s00493-022-4901-x42:Suppl 2(1385-1408)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s00493-022-4901-x
Lejeune MRigo MRosenfeld M(2020)Templates for the k-binomial complexity of the Tribonacci wordAdvances in Applied Mathematics10.1016/j.aam.2019.101947112(101947)Online publication date: Jan-2020
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Lietard FRosenfeld M(2020)Avoidability of Additive Cubes over Alphabets of Four NumbersDevelopments in Language Theory10.1007/978-3-030-48516-0_15(192-206)Online publication date: 11-May-2020
https://dl.acm.org/doi/10.1007/978-3-030-48516-0_15
Chen JWen ZWu W(2019)On the additive complexity of a Thue–Morse-like sequenceDiscrete Applied Mathematics10.1016/j.dam.2019.01.008Online publication date: Feb-2019
https://doi.org/10.1016/j.dam.2019.01.008
Lejeune MRigo MRosenfeld M(2019)Templates for the k-Binomial Complexity of the Tribonacci WordCombinatorics on Words10.1007/978-3-030-28796-2_19(238-250)Online publication date: 9-Sep-2019
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Rao MRosenfeld M(2018)Avoiding Two Consecutive Blocks of Same Size and Same Sum over $\mathbb{Z}^2$SIAM Journal on Discrete Mathematics10.1137/17M114937732:4(2381-2397)Online publication date: 4-Oct-2018
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Ochem PRao MRosenfeld M(2018)Avoiding or Limiting Regularities in WordsSequences, Groups, and Number Theory10.1007/978-3-319-69152-7_5(177-212)Online publication date: 10-Apr-2018
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Du CMousavi HRowland ESchaeffer LShallit J(2017)Decision algorithms for Fibonacci-automatic words, IITheoretical Computer Science10.1016/j.tcs.2016.10.005657:PB(146-162)Online publication date: 2-Jan-2017
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Rigo M(2017)Relations on wordsIndagationes Mathematicae10.1016/j.indag.2016.11.01828:1(183-204)Online publication date: Feb-2017
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On enumeration of pattern-avoiding Fishburn permutations

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On enumeration of pattern-avoiding Fishburn permutations

The equidistribution of some Mahonian statistics over permutations avoiding a pattern of length three

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