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Secant Tree Calculus

A true Tree Calculus is being developed to make a joint study of the two statistics &#34;eoc&#34; (end of minimal chain) and &#34;pom&#34; (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.