Secant tree calculus

Dominique Foata; Guo-Niu Han

Open Mathematics (2014)

  • Volume: 12, Issue: 12, page 1852-1870
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Dominique Foata, and Guo-Niu Han. "Secant tree calculus." Open Mathematics 12.12 (2014): 1852-1870. <http://eudml.org/doc/268996>.

@article{DominiqueFoata2014,
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.},
author = {Dominique Foata, Guo-Niu Han},
journal = {Open Mathematics},
keywords = {Tree Calculus; Partial difference equations; Binary increasing labeled trees; Secant and tangent trees; End of minimal chain; Parent of maximum leaf; Bivariate distributions; Secant numbers; Entringer distribution; Alternating permutations; tree calculus; partial difference equations; binary increasing labeled trees; secant and tangent trees; end of minimal chain; parent of maximum leaf; bivariate distributions; secant numbers; alternating permutations},
language = {eng},
number = {12},
pages = {1852-1870},
title = {Secant tree calculus},
url = {http://eudml.org/doc/268996},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Dominique Foata
AU - Guo-Niu Han
TI - Secant tree calculus
JO - Open Mathematics
PY - 2014
VL - 12
IS - 12
SP - 1852
EP - 1870
AB - 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.
LA - eng
KW - Tree Calculus; Partial difference equations; Binary increasing labeled trees; Secant and tangent trees; End of minimal chain; Parent of maximum leaf; Bivariate distributions; Secant numbers; Entringer distribution; Alternating permutations; tree calculus; partial difference equations; binary increasing labeled trees; secant and tangent trees; end of minimal chain; parent of maximum leaf; bivariate distributions; secant numbers; alternating permutations
UR - http://eudml.org/doc/268996
ER -

References

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