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math.CO2015
On the density of the odd values of the partition function
Samuel D. Judge, William J. Keith, Fabrizio Zanello
The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the…
math.CO2015
Partitions into a small number of part sizes
William J. Keith
We study , the number of partitions of into part sizes, and find numerous arithmetic progressions where and take on values divisible by 2 and 4. Expandi…