It's true that U(m+p, p) >= U(m, p) but you can't replace this with an equality. The smallest counterexample is U(2, 3) = 1 U(5, 3) = 5/4 The reduction you are thinking of has the partition 3 0 0 1 1 0 3 0 1 1 0 0 3 1 1 with minimal element 1. Here's the optimal partition 7/4 0 7/4 0 3/2 0 7/4 0 7/4 3/2 5/4 5/4 5/4 5/4 0 Veit On Jan 16, 2009, at 8:51 AM, Andy Latto wrote:
If we have M muffins and P people, is the (a?) best answer for M+P muffins to give everyone 1 muffin and reduce to the M,P problem?
Isn't the dual to the original problem (that is, dividing 7 muffins among 4 people) a counterexample to this?
Andy
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