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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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On the parity of generalized partition functions
by
Jean-Louis Nicolas
University Claude Bernard, Lyon, France
Coauthors: András Sárközy (Eötvös Loránd University, Budapest, Hungary)

Let A={a1 < a2 < ... } be a set of positive integers and A(x) its counting function. Let us denote by pA(n) the number of partitions of n with parts in A. Improving on a preceding paper jointly written with I.Z. Rusza (J.N.T. 1998), we show that there exists a set A satisfying A(x) > x/(logx)c , c < 1, such that, for n large enough, pA(n) is always even.

Date received: March 7, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-58.