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Abstract for 
David A. Bressoud, The Borwein Conjecture and Partitions with
Prescribed Hook Differences

 Peter Borwein has conjectured that certain polynomials
have non-negative coefficients. In this paper we look at some generalizations
of this conjecture and observe how they relate to the study of generating
functions for partitions with prescribed hook differences. A
combinatorial proof of the generating function for partitions with
prescribed hook differences is given.





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