A generator of morphisms for infinite words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, p. 427-441
We present an algorithm which produces, in some cases, infinite words avoiding both large fractional repetitions and a given set of finite words. We use this method to show that all the ternary patterns whose avoidability index was left open in Cassaigne’s thesis are 2-avoidable. We also prove that there exist exponentially many 7 4 + -free ternary words and 7 5 + -free 4-ary words. Finally we give small morphisms for binary words containing only the squares 0 2 , 1 2 and (01) 2 and for binary words avoiding large squares and fractional repetitions.
@article{ITA_2006__40_3_427_0,
     author = {Ochem, Pascal},
     title = {A generator of morphisms for infinite words},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {3},
     year = {2006},
     pages = {427-441},
     doi = {10.1051/ita:2006020},
     zbl = {1110.68122},
     mrnumber = {2269202},
     language = {en},
     url = {http://http://www.numdam.org/item/ITA_2006__40_3_427_0}
}
Ochem, Pascal. A generator of morphisms for infinite words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 3, pp. 427-441. doi : 10.1051/ita:2006020. http://www.numdam.org/item/ITA_2006__40_3_427_0/

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