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ON THE NUMBER OF NEARLY SELF-CONJUGATE PARTITIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 108 / Issue 1 / August 2023
- Published online by Cambridge University Press:
- 11 November 2022, pp. 114-119
- Print publication:
- August 2023
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- Article
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A partition
$\lambda $ of n is said to be nearly self-conjugate if the Ferrers graph of 
$\lambda $ and its transpose have exactly 
$n-1$ cells in common. The generating function of the number of such partitions was first conjectured by Campbell and recently confirmed by Campbell and Chern (‘Nearly self-conjugate integer partitions’, submitted for publication). We present a simple and direct analytic proof and a combinatorial proof of an equivalent statement.
