On an algebraicity theorem of Kontsevich

Abstract

We give in a particular case a combinatorial proof of a recent algebraicity result of Kontsevich; the proof uses generalized one-sided and two-sided Dyck words, or equivalently, excursions and bridges. We indicate a non-commutative version of these notions, which could lead to a full proof. We show also a relation with pointed planar maps. © 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.