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math.CO2021
Combinatorial proofs of the Ramanujan type congruences modulo 3
Robert X. J. Hao
The partition statistic -rank is introduced to give combinatorial proofs of the Ramanujan type congruences mod 3 for certain classes of partition functions.
math.CO2021
A crank for bipartitions with designated summands
R. X. J. Hao, E. Y. Y. Shen
Andrews, Lewis and Lovejoy introduced the partition function as the number of partitions of with designated summands. A bipartition of is an ordered pair of partiti…