Asymptotic Oscillations and Binary Partitions of Integers

9:00 AM-9:45 AM

*Room: Capito Center/South*

*Chair: Carla Savage, North Carolina State University*

Among the most interesting asymptotic expansions in discrete mathematics are those that exhibit oscillatory behavior in some of their lower order terms. We'll give a brief survey of results of this type, followed by some new results, from joint work of Neil Calkin and myself. The latter refer to the function b(n), which is the number of partitions of n into powers of 2, in which the multiplicity of each part is at most 2. In addition to growth results about b(n) we will describe some binary trees that it generates and which have interesting properties.

**Herbert S. Wilf**

*Thomas A. Scott Professor of Mathematics*

*Department of Mathematics*

*University of Pennsylvania*

*MMD, 2/2/99*