Catalan fragile words

[1] S. V. Al¨eshin, A free group of finite automata, Mosc. Univ. Math. Bull., 38 (1983) 10–13.

[2] B. Bollob´as, Modern graph theory, Graduate Texts in Mathematics, 184, Springer-Verlag, New York, 1998.

[3] L. Bartholdi, R. Grigorchuk and V. Nekrashevych, From fractal groups to fractal sets, Fractals in Graz 2001,
Trends Math., Birkh¨auser Basel, (2003) 25–118.

[4] D. D’Angeli and E. Rodaro, Fragile words and Cayley type transducers, Int. J. Group Theory, 7 no. 3 (2018)
91–109.

[5] S. Eilenberg, Automata, Languages and Machines, A, Pure and Applied Mathematics, 58, Academic Press [A
subsidiary of Harcourt Brace Jovanovich, Publishers], New York, 1974.

[6] R. Grigorchuk, V. Nekrashevych and V. Sushchanskii, Automata, dynamical systems and infinite groups, Proc.
Steklov Inst. Math., 231 (2000) 134–214.

[7] R. Grigorchuk, Some topics of dynamics of group actions on rooted trees, Proc. Steklov Inst. Math., 273 (2011)
64–175.

[8] V. Nekrashevych, Self-similar groups, Mathematical Surveys and Monographs, 117, American Mathematical Society, Providence, RI, 2005.

[9] S. Roman, An introduction to Catalan numbers, Compact textbooks in Mathematics, Birkhauser, Basel, 2005.

[10] B. Steinberg, M. Vorobets and Y. Vorobets, Automata over a binary alphabet generating free groups of even rank,
Int. J. Algebra Comput., 21 (2011) 329–354.

[11] M. Vorobets and Y. Vorobets, On a free group of transformations defined by an automaton, Geom. Dedicata, 124
(2007) 237–249.

[12] M. Vorobets and Y. Vorobets, On a series of finite automata defining free transformation groups, Groups Geom.
Dyn., 4 (2010) 377–405.