Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(6), 220-222
DOI: 10.12691/tjant-2-6-5
Open AccessArticle

Note on a Partition Function Which Assumes All Integral Values

Manvendra Tamba1,

1Department of Mathematics, Goa University, Taleigao Plateau, Goa, India

Pub. Date: November 27, 2014

Cite this paper:
Manvendra Tamba. Note on a Partition Function Which Assumes All Integral Values. Turkish Journal of Analysis and Number Theory. 2014; 2(6):220-222. doi: 10.12691/tjant-2-6-5

Abstract

Let G(n) denote the number of partitions of n into distinct parts which are of the form 2m, 3m, 5m, 6m-3, 8m-3, 9m-3 or 11m-3 with parts of the form 2m, 3m, 6m-3, or 11m-3 being even in number minus the number of them with parts of the form 2m, 3m, 6m-3, or 11m-3 being odd in number. In this paper, we prove that G(n) assumes all integral values and does so infinitely often.

Keywords:
partition functions Gaussian integers Jacobi’s triple product identity

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References:

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