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.
@article{bwmeta1.element.doi-10_2478_s11533-014-0429-7,
author = {Dominique Foata and Guo-Niu Han},
title = {Secant tree calculus},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1852-1870},
zbl = {1297.05017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0429-7}
}
Dominique Foata; Guo-Niu Han. Secant tree calculus. Open Mathematics, Tome 12 (2014) pp. 1852-1870. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0429-7/
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