The Borwein Conjecture and Partitions with Prescribed Hook Differences

David A. Bressoud

Abstract


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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