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Secant tree calculus

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Central European Journal of Mathematics

Abstract

A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.

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Authors and Affiliations

  1. Institut Lothaire, 1, rue Murner, F-67000, Strasbourg, France

    Dominique Foata

  2. I.R.M.A. UMR 7501, Université de Strasbourg et CNRS, 7, rue René-Descartes, F-67084, Strasbourg, France

    Guo-Niu Han

Authors
  1. Dominique Foata
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  2. Guo-Niu Han
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Correspondence to Dominique Foata.

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Foata, D., Han, GN. Secant tree calculus. centr.eur.j.math. 12, 1852–1870 (2014). https://doi.org/10.2478/s11533-014-0429-7

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  • DOI: https://doi.org/10.2478/s11533-014-0429-7

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