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Lewis, Richard (1997) The ranks of partitions modulo 2. Discrete Mathematics, 167. pp. 445-449. ISSN 0012-365X
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Official URL: http://dx.doi.org/10.1016/S0012-365X(96)00246-4
Abstract
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 |
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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 |
URI: | http://sro.sussex.ac.uk/id/eprint/27588 |