Estimates of five restricted partition functions that are quasi polynomials

Bulletin of Mathematical Sciences - Tập 5 - Trang 1-11 - 2014
A. David Christopher1, M. Davamani Christober1
1Department of Mathematics, The American College, Madurai, India

Tóm tắt

A function defined on is said to be a quasi polynomial if, is a polynomial in for each , where is a positive integer. In this article, we show that the below given restricted partition functions are quasi polynomials: (i) -number of partitions of with exactly parts and least part being less than , (ii) -number of distinct partitions (partitions with distinct parts) of with exactly parts and least part being less than , (iii) -number of partitions of with exactly parts and least parts, (iv) -number of partitions of with exactly parts and one largest part and (v) -number of partitions of with exactly parts and difference between least part and largest part exceeds . Consequently, following estimates were derived: (i) (ii) (iii) (iv) (v)

Tài liệu tham khảo

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