13th Erdos Colloquium
Professor George E. Andrews *
The Pennsylvania State University
Partition Function Differences, Ehrenpreis's Problem and a New/Old Method
Abstract: For decades partition function differences have been studied. These include a famous problem of Henry Alder posed in the 1950's and solved only recently by Yee, Oliver et al.. In 1978, Szekeres and Richmond partially solved a problem of this type concerning the Rogers-Ramanujan continued fraction. Unknown to them, the problem had essentially been solved by Ramanujan in the Lost Notebook. In this talk, I will begin with the history of such problems. I will conclude with some observations on a general method for treating some such problems.
Here is a typical example of the questions posed. The late Leon Ehrenpreis asked in 1987 if one could prove that the number of partitions of n into parts congruent to 1 or 4 mod 5 is always at least as large as the number with parts congruent to 2 or 3 mod 5 WITHOUT using the Rogers-Ramanujan identities. Subsequently Baxter and I gave a "sort of" solution to the problem, and Kevin Kadell gave a complete solution in 1999.
In a long and distinguished career spanning several decades, Professor Andrews has received numerous recognitions, including the Guggenheim Fellowship in 1982-82, the invitation to give the Hedrick Lectures for the Mathematical Association of America in 1980, the election to the American Academy of Arts and Sciences in 1997, the award of an Honorary Doctorate by the University of Florida in 2002, and the election to the National Academy of Sciences in 2004.
He is the current President of the American Mathematical Society.
Created Friday, January 28, 2011.
Last update made Fri Jan 28 12:19:38 EST 2011.