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The ranks of partitions modulo 2

journal contribution
posted on 2023-06-08, 07:26 authored by Richard Lewis
Let N(0, 2, n), respectively N(1, 2, n), denote the number of partitions of n whose ranks are even, respectively odd. We show here that N(0, 2, n) < N(1, 2, n), when n is even, and that this inequality is reversed, when n is odd. Our proof is ‘bijective’ in that we construct an injective map between the sets of partitions involved. We use a variation of the Involution Principle of Garsia and Milne.

History

Publication status

  • Published

Journal

Discrete Mathematics

ISSN

0012-365X

Publisher

Elsevier

Volume

167

Page range

445-449

ISBN

0024-6093

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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