Speaker: Zoran Sunik, Texas A&M University
Title: The Catalan family tree, Young tableaux, and tree endomorphisms
Abstract: We introduce the Catalan family tree and show that its vertices are precisely the fixed points of a certain tree endomorphism. In a similar fashion, Young tableaux represent the double points of another tree endomorphism. Both tree endomorphisms have natural descriptions as transformations of integer sequences. The members of the Catalan family tree correspond to self-describing integer sequences, while pairs of conjugated Young tableaux correspond to pairs of mutually describing sequences.