Théorie combinatoire des T-fractions et approximants de Padé en deux points Original Research Article

We present a combinatorial interpretation for Thronʹs continued fractions (T-fractions) in terms of labelled Dyck paths. The links between convergents of T-fractions and two points Padé approximants arise naturally. Then we show a new bijection between permutations and some combinatorial histories, allowing us to compute the generating function of a trivariate statistics on permutations. Finally, a strange application of the duality of T-fractions is given.