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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Coefficients associated with the expansion of certain products


Author: D. P. Roselle
Journal: Proc. Amer. Math. Soc. 45 (1974), 144-150
MSC: Primary 05A10
DOI: https://doi.org/10.1090/S0002-9939-1974-0342406-X
MathSciNet review: 0342406
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Abstract: Simple combinatorial interpretations are given for the coefficients of the polynomials $ {H_n}(x,y)$ and $ {G_n}(x,y)$ defined by $ \prod (1 + {x^n}{y^m}t) = \Sigma {G_n}(x,y){t^n}/{(x)_n}{(y)_n}$ and $ \prod {(1 - {x^n}{y^m}t)^{ - 1}} = \Sigma {H_n}(x,y){t^n}/{(x)_n}{(y)_n}$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0342406-X
Article copyright: © Copyright 1974 American Mathematical Society