Abstract: In 1987, George Andrews considered the following question: For which sets of positive integers S and T is p(S; n) = p(T; n-1) f or all n>1?, where p(S; n) denotes the number of partitions of n into elements of S. Andrews found two non-trivial examples and found a further six. We prove a new shifted partition identity using the theory of modular functions. We consider other shifted-type identities and shiftless identities. Let a be a fixed positive integer, and let S, T be distinct sets of positive integers. A shiftless identity has the form: p(S; T) = p(T; n) for all n not equal to a. These other identities arise through certain modular transformations.

The url of this page is http://www.math.ufl.edu/~frank/abstracts/shifted.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Wednesday, March 13, 2002.
Last update made Wed Mar 13 14:39:14 EST 2002.

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