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{\bf Piotr \'Sniady}
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{\bf Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective proof of generalized Cauchy identities}
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In this series of articles we study connections between combinatorics
of multidimensional generalizations of the 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 the
multidimensional generalizations of the Cauchy identity. Our
bijection uses oriented planar trees equipped with some linear
orders.
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