University of Isfahan International Journal of Group Theory 2251-7650 9 2 2020 06 01 Catalan fragile words 69 80 23435 10.22108/ijgt.2019.113180.1506 EN Daniele D'Angeli TUGraz Alfredo Donno Università degli Studi Niccolò Cusano Dipartimento di Ingegneria Via Don Carlo Gnocchi, 3 00166 Roma, Italy Emanuele Rodaro Dipartimento di Matematica, Politecnico di Milano, Milano, Italia Journal Article 2018 10 03 ‎Fragile words have been already considered in the context of automata groups‎. ‎Here we focus our attention on a special class of strongly fragile words that we call Catalan fragile words‎. ‎Among other properties‎, ‎we show that there exists a one-to-one correspondence between the set of Catalan fragile words and the set of full binary trees‎. Automata group Catalan number Fragile word Full binary tree https://ijgt.ui.ac.ir/article_23435_55a44b9deabef92baa68e39860e518aa.pdf