Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities
Abstract
Description
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.
Version 2: numerous misprints were corrected. Version 3: bijections described in an algorithmic way
Version 2: numerous misprints were corrected. Version 3: bijections described in an algorithmic way