PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Title:Congruences Modulo High Powers of 2 for Sloaneā€™s Box Stacking Function
Seminar:Combinatorics/Partitions Seminar
Speaker:Dr. James Sellers, Department of Mathematics, The Pennsylvania State University
Abstract:
The focus of this talk will be on congruences satisfied by various integer partition functions. I will share some history, starting with R.F. Churchhouse's work in the late 1960's on the binary partition function. I will also discuss work of Rodseth, Andrews, and Gupta in the 1970's on results for m-ary partitions which are natural generalizations of binary partitions.(An m-ary partition of a positive integer n is a nonincreasing sequence of powers of m which sum to n. So, for example, 9+9+3+1+1+1 is a 3-ary partition of the integer 24.) I will then discuss work I completed with Rodseth (in the last decade or so) which generalizes the results of Andrews and Gupta from the 1970's. I will close with a set of "applications" of m-ary partitions to Neil Sloane's questions on non-squashing stacks of boxes, along with extremely new results obtained with Rodseth which have recently been accepted for publication. The talk will be self-contained and geared for a general audience.

Room Reservation Information

Room Number:MB106
Date:10 / 14 / 2008
Time:11:15am - 12:05pm