Hereditary properties of words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 49-65.

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 mn words of length n then, for every kn+m, it contains at most (m+1)/2(m+1)/2 words of length k.

DOI : 10.1051/ita:2005003
Classification : 05C
Mots-clés : graph properties, monotone, hereditary, speed, size
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Balogh, József; Bollobás, Béla. Hereditary properties of words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 49-65. doi : 10.1051/ita:2005003. http://www.numdam.org/articles/10.1051/ita:2005003/

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