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CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
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A well-known problem regarding the integer partition function p(n) is the parity problem, how often is p(n) even or odd? Motivated by this problem, we obtain the following results: (1) A generating function for the number of crank 0 partitions of n. (2) An involution on the crank 0 partitions whose fixed points are called invariant partitions. We then derive a generating function for the number of invariant partitions. (3) A generating function for the number of self-conjugate rank 0 partitions.
Title: CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
Description:
A well-known problem regarding the integer partition function p(n) is the parity problem, how often is p(n) even or odd? Motivated by this problem, we obtain the following results: (1) A generating function for the number of crank 0 partitions of n.
(2) An involution on the crank 0 partitions whose fixed points are called invariant partitions.
We then derive a generating function for the number of invariant partitions.
(3) A generating function for the number of self-conjugate rank 0 partitions.
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