The ranks of partitions modulo 2

Lewis, Richard (1997) The ranks of partitions modulo 2. Discrete Mathematics, 167. pp. 445-449. ISSN 0012-365X

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: EPrints Services
Date Deposited: 06 Feb 2012 20:42
Last Modified: 10 Jul 2012 11:24
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