License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2018.54
URN: urn:nbn:de:0030-drops-84976
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8497/
Rajasekaran, Aayush ;
Shallit, Jeffrey ;
Smith, Tim
Sums of Palindromes: an Approach via Automata
Abstract
Recently, Cilleruelo, Luca, & Baxter proved, for all bases b >= 5, that every natural number is the sum of at most 3 natural numbers whose base-b representation is a palindrome. However, the cases b = 2, 3, 4 were left unresolved. We prove, using a decision procedure based on automata, that every natural number is the sum of at most 4 natural numbers whose base-2 representation is a palindrome. Here the constant 4 is optimal. We obtain similar results for bases 3 and 4, thus completely resolving the problem.
BibTeX - Entry
@InProceedings{rajasekaran_et_al:LIPIcs:2018:8497,
author = {Aayush Rajasekaran and Jeffrey Shallit and Tim Smith},
title = {{Sums of Palindromes: an Approach via Automata}},
booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
pages = {54:1--54:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-062-0},
ISSN = {1868-8969},
year = {2018},
volume = {96},
editor = {Rolf Niedermeier and Brigitte Vall{\'e}e},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8497},
URN = {urn:nbn:de:0030-drops-84976},
doi = {10.4230/LIPIcs.STACS.2018.54},
annote = {Keywords: finite automaton, nested-word automaton, decision procedure, palindrome, additive number theory}
}
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Keywords: |
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finite automaton, nested-word automaton, decision procedure, palindrome, additive number theory |
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Collection: |
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35th Symposium on Theoretical Aspects of Computer Science (STACS 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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27.02.2018 |
