Fraenkel's Conjecture on Divisibility of the Ternary Partition Function

Combinatorics/Partitions Seminar

Meeting Details

For more information about this meeting, contact Matthew Katz, James Sellers, George Andrews.

Speaker: James Sellers, PSU

Abstract: In this talk, we will focus our attention on m-ary partitions which are integer partitions wherein each part must be a power of a fixed integer m>1. Since the late 1960s, numerous mathematicians (including Churchhouse, Andrews, Gupta, Rodseth, and Sellers) have studied divisibility properties of m-ary partitions. In this talk, I will describe a novel and unexpected conjecture communicated to me by Aviezri Fraenkel which characterizes the divisibility of the ternary partition function b_3(n) based on the base 3 representation of n. I will provide a proof of this result, and will close with a wonderful generalization that follows quite naturally. This is joint work with George Andrews.

Room Reservation Information

Room Number: 106 McAllister

Date: 10/29/2013

Time: 10:10am - 11:00am