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).