Document Type

Article

Publication Date

2015

Abstract

We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if (q r−tk, qmk−(r−tk) ; q mk)∞ (q r, qmk−r; qmk)∞ =: X∞ n=0 cnq n , for certain integers k, m s and t, where r = sm+t, then ckn−rs is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also give results for cases not covered by the theorems of Alladi and Gordon. We also give some interpretations of the analytic results in terms of integer partitions.

Publication Title

Journal of the Australian Mathematical Society

ISSN

1446-7887

Publisher

Australian Mathematical Society

Volume

98

Issue

1

Comments

Preprint version is available here.

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