James Sellers

Affiliation: Penn State University

Email: sellersj@math.psu.edu

Title Of Talk: Elementary proofs of parity results for 5--regular partitions

Abstract: In a paper which appeared in late 2008, Calkin, Drake, James, Law, Lee, Penniston and Radder use the theory of modular forms to examine 5--regular partitions modulo 2 and 13--regular partitions modulo 2 and 3. They obtain and conjecture various results. In this note, we use nothing more than Jacobi's triple product identity to obtain results for 5--regular partitions stronger than those obtained by Calkin and his collaborators. In particular, we find infinitely many Ramanujan--type congruences for $b_5(n)$ in a straightforward manner relying on an easily--proven relationship between $b_5(4n+1)$ and the number of representations of an integer by the quadratic form $2x^2+5y^2.$ This is joint work with Michael Hirschhorn of the University of New South Wales.

Last update made Wed Feb 11 11:48:14 EST 2009.
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