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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. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures. [ABSTRACT FROM AUTHOR]