##### on the course to be submitted for publication.

# Dominique Foata, Guo-Niu Han

#
TREE CALCULUS FOR BIVARIABLE DIFFERENCE EQUATIONS

**Abstract.**
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, ``end of minimal chain'' and ``parent of maximum leaf'' a true Tree Calculus is being developed
to solve a partial difference equation system and then make a joint study of those two statistics. Their joint distribution is shown to be symmetric and to be expressed in the form of an explicit three-variable generating function.

foata at unistra dot fr,
guoniu dot han at unistra dot fr

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