ON THE PARITY OF PARTITION FUNCTIONS
2003 ◽
Vol 14
(04)
◽
pp. 437-459
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Keyword(s):
Let S denote a subset of the positive integers, and let pS(n) be the associated partition function, that is, pS(n) denotes the number of partitions of the positive integer n into parts taken from S. Thus, if S is the set of positive integers, then pS(n) is the ordinary partition function p(n). In this paper, working in the ring of formal power series in one variable over the field of two elements Z/2Z, we develop new methods for deriving lower bounds for both the number of even values and the number of odd values taken by pS(n), for n ≤ N. New very general theorems are obtained, and applications are made to several partition functions.
1968 ◽
Vol 9
(2)
◽
pp. 146-151
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2003 ◽
Vol 75
(1)
◽
pp. 1-7
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2019 ◽
Vol 150
(1)
◽
pp. 1-16
2003 ◽
Vol 184
(2)
◽
pp. 369-383
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Keyword(s):
2004 ◽
Vol 339
(8)
◽
pp. 533-538
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2002 ◽
Vol 51
(3)
◽
pp. 403-410
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2017 ◽
Vol 2018
(15)
◽
pp. 4780-4798
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Keyword(s):