**
John
J.C.
Saunders,
Department
of
Pure
Mathematics,
University
of
Waterloo**

“Random Fibonacci Sequences”

We study here the random fibonacci tree, which is an infinite binary tree with non-negative numbers at each node defined as follows. The root consists of the number 1 with a single child also the number 1. Then we define the tree recursively in the following way: if x is the parent of y, then y has two children, namely |x − y| and x + y. This tree was studied by Benot Rittaud who proved that any pair of integers a, b that are coprime occur together on a single branch of this tree and that such occurances are infinite. In particular, this is true for the pair (1, 1). We extend his results by giving bounds on the number of such occurances at any specific level down the tree, as well as prove other interesting results dealing with these (1, 1) pairs. This is joint work with Kevin Hare.

MC 5479