Catalan fragile words

Abstract

‎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.

Keywords

• automata group
• catalan number
• fragile word
• full binary tree