Avoidability of Additive Cubes over Alphabets of Four Numbers

Let [Formula: see text] be a set of size 4 such that [Formula: see text] cannot be obtained by applying the same affine function to all of the elements of [Formula: see text]. We show that there is an infinite sequence of elements of [Formula: see text] that contains no three consecutive blocks of s...

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Autores principales: Lietard, Florian, Rosenfeld, Matthieu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7247873/
http://dx.doi.org/10.1007/978-3-030-48516-0_15
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author Lietard, Florian
Rosenfeld, Matthieu
author_facet Lietard, Florian
Rosenfeld, Matthieu
author_sort Lietard, Florian
collection PubMed
description Let [Formula: see text] be a set of size 4 such that [Formula: see text] cannot be obtained by applying the same affine function to all of the elements of [Formula: see text]. We show that there is an infinite sequence of elements of [Formula: see text] that contains no three consecutive blocks of same size and same sum (additive cubes). Moreover, it is possible to replace [Formula: see text] by [Formula: see text] in the statement.
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spelling pubmed-72478732020-05-26 Avoidability of Additive Cubes over Alphabets of Four Numbers Lietard, Florian Rosenfeld, Matthieu Developments in Language Theory Article Let [Formula: see text] be a set of size 4 such that [Formula: see text] cannot be obtained by applying the same affine function to all of the elements of [Formula: see text]. We show that there is an infinite sequence of elements of [Formula: see text] that contains no three consecutive blocks of same size and same sum (additive cubes). Moreover, it is possible to replace [Formula: see text] by [Formula: see text] in the statement. 2020-05-26 /pmc/articles/PMC7247873/ http://dx.doi.org/10.1007/978-3-030-48516-0_15 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Lietard, Florian
Rosenfeld, Matthieu
Avoidability of Additive Cubes over Alphabets of Four Numbers
title Avoidability of Additive Cubes over Alphabets of Four Numbers
title_full Avoidability of Additive Cubes over Alphabets of Four Numbers
title_fullStr Avoidability of Additive Cubes over Alphabets of Four Numbers
title_full_unstemmed Avoidability of Additive Cubes over Alphabets of Four Numbers
title_short Avoidability of Additive Cubes over Alphabets of Four Numbers
title_sort avoidability of additive cubes over alphabets of four numbers
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7247873/
http://dx.doi.org/10.1007/978-3-030-48516-0_15
work_keys_str_mv AT lietardflorian avoidabilityofadditivecubesoveralphabetsoffournumbers
AT rosenfeldmatthieu avoidabilityofadditivecubesoveralphabetsoffournumbers

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