Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities

Details Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities

2004-12-02

arxiv.org/abs/math/0412043v3

Electron. J. Combin. 13(1), 2006, Research Paper 62

Mathematics

Combinatorics

Version 2: numerous misprints were corrected. Version 3: bijections described in an algorithmic way

Scientific paper

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.

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