A Family of Combinatorial Identities

Author:

Andrews G. E.,Subbarao M. V.,Vidyasagar M.

Abstract

In a recent paper, Murray Eden [5] generalized the simple identity for the Eulerian product,1.1and obtained the following infinite family of identities:For A= 1,2, 3,…, let1.2where we assume throughout that |x| < 1, empty products equal unity and empty sums equal zero; then1.3As Eden noted, Fh(b;x) is the generating function of ph(m, n) which denotes the number of partitions of n into m parts, in which the largest part appears exactly h times and all other parts are distinct:

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Positive differences of overpartitions with separated parts;The Ramanujan Journal;2023-12-28

2. The asymptotic distribution of the rank for unimodal sequences;Journal of Number Theory;2021-12

3. A Note on Andrews’ Partitions with Parts Separated by Parity;Annals of Combinatorics;2019-10-16

4. Some Remarks on a Product Expansion;Developments in Mathematics;2001

5. On the paper “A ‘lost’ notebook of Ramanujan”;Advances in Mathematics;1984-09

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