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A Family of Combinatorial Identities

Published online by Cambridge University Press:  20 November 2018

G. E. Andrews ,
M. V. Subbarao  and
M. Vidyasagar
G. E. Andrews
Affiliation:
Pennsylvania State University, University park, Pennsylvania
M. V. Subbarao
Affiliation:
Pennsylvania State University, University park, Pennsylvania
M. Vidyasagar
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts
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In a recent paper, Murray Eden [5] generalized the simple identity for the Eulerian product,

1.1

and obtained the following infinite family of identities:

For A= 1,2, 3,…, let

1.2

where we assume throughout that |x| < 1, empty products equal unity and empty sums equal zero; then

1.3

As 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:

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 11 - 18
Copyright
Copyright © Canadian Mathematical Society 1972

References

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