Thursday, July 17, 2025 - 16:15 in U2-232
Catalan sums, meandric systems and 1/Pi
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Paul Thévenin from Uni Angers
| Abstract: |
We investigate a family of infinite sums of products of Catalan numbers, indexed by trees.
These sums naturally appear in the study of combinatorial structures called meandric systems, which are configurations of non-crossing loops in the plane.
We show that these sums are all polynomials in 1/Pi with rational coefficients.
We also construct an algorithm to compute them, based on induction on the size of the trees and properties of standard hypergeometric functions.
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