Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities
Combinatorics
2007-05-23 v3 Probability
Abstract
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.
Keywords
Cite
@article{arxiv.math/0412043,
title = {Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities},
author = {Piotr Sniady},
journal= {arXiv preprint arXiv:math/0412043},
year = {2007}
}
Comments
Version 2: numerous misprints were corrected. Version 3: bijections described in an algorithmic way