Generalized Cauchy identities, trees and multidimensional Brownian   motions. Part I: bijective proof of generalized Cauchy identities
  In this series of articles we study connections between combinatorics of multidimensional generalizations of Cauchy identity and continuous objects such as multidimensional Brownian motions and Brownian bridges.   In Part I of the series we present a bijective proof of multidimensional generalizations of the Cauchy identity. Our bijection uses oriented planar trees equipped with some linear orders. 
Piotr Sniady