CONGRUENCES FOR RANKS OF PARTITIONS

Author:

MAO RENRONG

Abstract

Abstract Ranks of partitions play an important role in the theory of partitions. They provide combinatorial interpretations for Ramanujan’s famous congruences for partition functions. We establish a family of congruences modulo powers of $5$ for ranks of partitions.

Publisher

Cambridge University Press (CUP)

Reference18 articles.

1. Asymptotics for rank partition functions;Bringmann;Trans. Amer. Math. Soc.,2009

2. Congruences modulo powers of 5 for the rank parity functions;Chen;Hardy-Ramanujan J.,2020

3. New equalities and inequalities for the ranks and cranks of partitions;Fan;Adv. Appl. Math.,2023

4. The Andrews–Sellers family of partition congruences;Paule;Adv. Math.,2012

5. Inequalities for differences of Dyson’s rank for all odd moduli;Bringmann;Math. Res. Lett.,2010

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