Talk:Rearrangement inequality

I'm unsure about the General Rearrangement Inequality: is it true for n > 3 or not? The article says there counterexamples -- specifically, from the history page it is clear that User:Maxal says that there are counterexamples. Maxal, could you provide some? For, say, n = 4? And if it's not true, then why state it for general n? (Frankly, why state it at all? Since the statement is trivial for n = 2 (and of course n = 1), so it only says something for n = 3. So, in any case, it should be rephrased.)


 * For n=4, a particular counterexample is given by two sets of integers 0,1,2,3 and 0,1,2,10 for which:
 * $$0\cdot0+1\cdot1+2\cdot10+3\cdot2=27 < 31= 0\cdot 2+1\cdot 1+2\cdot 0+3\cdot 10$$
 * It can be easily extended to n greater than 4. This incorrect attempted generalization deserves to be mentioned since it was published in a respected journal. Maxal (talk) 17:48, 31 March 2010 (UTC)

Aikhrabrov (talk) 22:33, 13 October 2010 (UTC)
 * For n=3 this inequality is trivial too: it is classical rearrangement inequality fot n=3 or n=2. Article with incorrect inequality wasn't in mathematical journal, so there is no need for mentioning this generalization at all.