ON THE FIRST AND SECOND MOMENTS OF PARITY BIAS IN INTEGER PARTITIONS

Byungchan Kim

doi:10.4134/BKMS.b250261

ON THE FIRST AND SECOND MOMENTS OF PARITY BIAS IN INTEGER PARTITIONS

Byungchan Kim

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let p(m, n) be the number of partitions of n with m more odd parts than even parts. We consider the first and second moment of p(m, n) and p(m, n) − p(−m, n) to further investigate parity bias in integer partitions. We give the generating functions for these moments and derive asymptotic formulas by employing Wright’s circle method.

Original language	English
Pages (from-to)	829-839
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	63
Issue number	3
DOIs	https://doi.org/10.4134/BKMS.b250261
State	Published - May 2026

Keywords

Parity bias
Wright’s circle method
asymptotic mean
asymptotic variance
parity excess

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10.4134/BKMS.b250261

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abstract = "Let p(m, n) be the number of partitions of n with m more odd parts than even parts. We consider the first and second moment of p(m, n) and p(m, n) − p(−m, n) to further investigate parity bias in integer partitions. We give the generating functions for these moments and derive asymptotic formulas by employing Wright{\textquoteright}s circle method.",

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AB - Let p(m, n) be the number of partitions of n with m more odd parts than even parts. We consider the first and second moment of p(m, n) and p(m, n) − p(−m, n) to further investigate parity bias in integer partitions. We give the generating functions for these moments and derive asymptotic formulas by employing Wright’s circle method.

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KW - Wright’s circle method

KW - asymptotic mean

KW - asymptotic variance

KW - parity excess

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ON THE FIRST AND SECOND MOMENTS OF PARITY BIAS IN INTEGER PARTITIONS

Abstract

Keywords

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