Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

Calculus on a tree
with applications
Igor Urbiha Department of Mathematics, Faculty of Science and Mathematics, University of Zagreb, Bijenička c. 30, HR10002 Zagreb, Croatia We describe simple algebraic operations with nodeweighted
complete infinite binary trees. A nodeweighted 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 nodeweighted complete infinite binary trees can be described
implicitly by algebraiclike 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 ^{1} D. Svrtan, I. Urbiha, Calculus
on a tree with applications to the SternBrocot tree., submitted. ^{2} D. H. Lehmer, On Stern's
diatomic series, Amer. Math. Monthly 36(1) (1929), 5967. ^{3} M. A. Stern, Ueber eine zahlentheoretische Funktion, Journal für
die reine und angewandte Mathematik 55 (1858) 193220. ^{4} R. L. Graham, D. E. Knuth, O.
Patashnik, Concrete Mathematics: A Foundation for Computer Science,
AddisonWesley, 2^{nd} edition, 1994. 