Ranks For Two Partition Quadruple Functions

2015/06/17 by Jennings-Shaffer, Chris
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1506.05354

Abstract

Recently the author introduced two new integer partition quadruple functions, which satisfy Ramanujan-type congruences modulo 3, 5, 7, and 13. Here we reprove the congruences modulo 3, 5, and 7 by defining a rank-type statistic that gives a combinatorial refinement of the congruences.

Related

• Combinatorial proofs of the Ramanujan type congruences modulo 3
• Two partition functions with congruences modulo 3, 5, 7, and 13
• Congruences modulo powers of 5 for the rank parity function
• Modulo 2 congruences for partitions with initial repetitions
• Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function