Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002



Calculus on a tree with applications


Igor Urbiha


Department of  Mathematics, Faculty of Science and  Mathematics, University of Zagreb, Bijenička c. 30, HR-10002 Zagreb, Croatia




We describe simple algebraic operations with node-weighted complete infinite binary trees. A node-weighted binary tree consists of a binary tree (its frame) and a function assigning to each node of the tree a number (its entry). (Note the analogy with an array and its entries.) Some particular node-weighted complete infinite binary trees can be described implicitly by algebraic-like equations which also exploit structure of a tree. Sometimes some deeper structural properties can be read out directly from such equations. As an illustration of this
formalism we give some structural and numerical properties of the Stern-Brocot tree and their relations to hyperbinary partition function and some number theoretic functions studied by Eisenstein, Stern, de Rham, Carlitz, Dijkstra.


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