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The ranks of partitions modulo 2
journal contribution
posted on 2023-06-08, 07:26 authored by Richard LewisLet 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.
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Publication status
- Published
Journal
Discrete MathematicsISSN
0012-365XPublisher
ElsevierExternal DOI
Volume
167Page range
445-449ISBN
0024-6093Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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