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Generalized digital trees and their difference-differential equations. (English) Zbl 0758.60015
From the authors’ abstract: Consider a tree partitioning process in which \(n\) elements are split into \(b\) at the root of a tree (\(b\) a design parameter), the rest going recursively into two subtrees with a binomial probability distribution. This extends some familiar tree data structures of computer science like the digital tree and the digital search tree. The exponential generating function for the expected size of the tree satisfies a difference-differential equation of order \(b\), \[ {d^ b \over dz^ b} f(z)=e^ z+2e^{z/2}f(z/2). \] The solution involves going to ordinary (rather than exponential) generating functions, analyzing singularities by means of Mellin transforms and contour integration.

60E10 Characteristic functions; other transforms
68R05 Combinatorics in computer science
60C05 Combinatorial probability
68R10 Graph theory (including graph drawing) in computer science
Full Text: DOI
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