8 Feb
2007
8 Feb
'07
7:01 p.m.
Alternative proof: suppose perm s <> 1, and let c denote the vector with components c_i. Then f(s) = |c|^2 cos(c, c') < |c|^2 = f(1), where c' is distinct from c and has the same length. WFL On 2/6/07, Daniel Asimov <dasimov@earthlink.net> wrote:
Given fixed real numbers c_1 < c_2 < . . . < c_n, define
f(sigma) = Sum_{1 <= j <= n} c_j c_sigma(j)
for any permutation sigma of {1,...,n}.
Prove that sigma = id_{1,...n} is the unique permutation that maximizes f(sigma).
--Dan
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