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Abstract
We relate the parity of the partition function to the parity of the
q -series
coefficients of certain powers of the modular discriminant using their generating
functions. This allows us to make statements about the parity of the initial values
of the partition function and to obtain a modified Euler recurrence for its
parity.
Keywords
partition, congruences
Mathematical Subject Classification 2000
Primary: 05A17
Milestones
Received: 3 August 2007
Revised: 28 October 2007
Accepted: 28 October 2007
Published: 28 February 2008
Communicated by Ken Ono