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Hereditary properties of words

Published online by Cambridge University Press:  15 March 2005

József Balogh  and
Béla Bollobás
József Balogh
Affiliation:
Department of Mathematical Sciences, The Ohio State University, Columbus, OH 43210, USA; [email protected]
Béla Bollobás
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, and Trinity College, Cambridge CB2 1TQ, England; [email protected]
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Abstract

Let P be a hereditary property of words, i.e., an infinite class of finite words such that every subword (block) of a word belonging to P is also in P. Extending the classical Morse-Hedlund theorem, we show that either P contains at least n+1 words of length n for every n or, for some N, it contains at most N words of length n for every n. More importantly, we prove the following quantitative extension of this result: if P has m ≤ n words of length n then, for every k ≥ n + m, it contains at most ⌈(m + 1)/2⌉⌈(m + 1)/2⌈ words of length k.

Keywords

Graph propertiesmonotonehereditaryspeedsize.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 49 - 65
Copyright
© EDP Sciences, 2005

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