Secant Tree Calculus

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.