title: The Andrews-Sellers family of partition congruences.
abstract: In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. In 2002 Dennis Eichhorn and Sellers were able to settle the conjecture for powers up to 4. In this article, we prove Sellers' conjecture for all powers of 5. In addition, we discuss why the Andrews-Sellers family is significantly different from classical congruences modulo powers of primes.
authors.affiliation: Research Institute for Symbolic Computation (RISC), Johannes Kepler University, A-4040 Linz, Austria.
authors.forename: Peter
authors.initials: P
authors.lastname: Paule
authors.forename: Cristian-Silviu
authors.initials: CS
authors.lastname: Radu
keywords: Generalized Frobenius partitions; Partition congruences of Ramanujan type; Sellers’ conjecture