Abstract
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doi:10.1016/S0012-365X(00)00294-6 
Copyright © 2001 Elsevier Science B.V. All rights reserved.
Note
Restricted bipartitions
Received 29 January 2000;
revised 15 May 2000;
accepted 16 June 2000
Available online 23 March 2001.
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Abstract
We consider bipartitions subject to certain restrictions and show that be(m,n)
bo(m,n), where be(m,n) (respectively, bo(m,n)) denotes the number of these partitions with an even (respectively, odd) number of even parts. Our principal tool is a lemma concerning the non-negativity of the coefficients of a certain rational function. As another corollary of this lemma, we deduce an inequality between the rank-counting numbers, N(r,m,n).
Corresponding author; email: r.p.lewis@sussex.ac.uk
