Tree-indexed Catalan sums

04.04.2024 14:30 - 15:30

Paul Thévenin (Uni Wien)

Abstract: A meandric system is a (topological) configuration of closed loops in the plane, which do not cross themselves nor each other. Motivated by the study of the structure of large meandric systems and of the so-called infinite noodle, we introduce and investigate sums of Catalan numbers associated to trees. It turns out that, surprisingly, all these sums are rational polynomials in 1/Pi. We will show on some examples where this comes from, and discuss connected results.

Based on an ongoing work with Alin Bostan (INRIA) and Valentin Féray (IECL).


SR 8, 2. OG, OMP 1