An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions

Combinatorics/Partitions Seminar

Meeting Details

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

Speaker: James Sellers, PSU

Abstract: In his 1984 AMS Memoir, George Andrews defined the family of $k$--colored generalized Frobenius partition functions. These are denoted by $c\phi_k(n)$ where $k\geq 1$ is the number of colors in question. In that Memoir, Andrews proved (among many other things) that, for all $n\geq 0,$ $c\phi_2(5n+3) \equiv 0\pmod{5}.$ Soon after, many authors proved congruence properties for various $k$--colored generalized Frobenius partition functions, typically with a small number of colors. In 2011, Baruah and Sarmah proved a number of congruence properties for $c\phi_4$, all with moduli which are powers of 4. In this brief note, we add to the collection of congruences for $c\phi_4$ by proving this function satisfies an unexpected result modulo 5. The proof is elementary, relying on Baruah and Sarmah's results as well as work of Srinivasa Ramanujan.

Room Reservation Information

Room Number: 106 McAllister

Date: 01/15/2013

Time: 11:15am - 12:05pm