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Jul
2
awarded  Curious
Feb
5
comment Where is the mistake in this argument about number of different balls with replacement
Thanks for the good write-up! I've got a better intuition of the situation now.
Feb
5
accepted Where is the mistake in this argument about number of different balls with replacement
Feb
5
comment Where is the mistake in this argument about number of different balls with replacement
Thanks for the answer. Yes that is my intuition too. However I fail to see how the events $D>0$ and $E_k$ are different. If $D>0$, if and only if there exists a $k$ such that $E_k$ is true.
Feb
5
asked Where is the mistake in this argument about number of different balls with replacement
Jan
31
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
30
comment Choosing the vector that minimizes this sum related to the rearrangement inequality
@PeterKoŇ°inár: I modified the statement slightly following our discussion and my experiments, and I think it is more correct now.
Jan
30
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
28
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
28
comment Choosing the vector that minimizes this sum related to the rearrangement inequality
@PeterKoŇ°inár: Yes it seems there are problems with small $n$. My intention is to work with big values of $n$, but this example is degenerated (but correct and helpful). The intuition here is that it is preferable, in order to minimize the sum, to pair big $x$'s with small $y$'s, in the same line of thought as the rearrangement inequality. In this case the sum cuts short too early for this strategy to prove useful. Perhaps the conjecture is only true for $n\to\infty$? (or perhaps is it not true at all)
Jan
27
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
26
comment Choosing the vector that minimizes this sum related to the rearrangement inequality
Thank you, I corrected the example. Regarding your example, we have $S([0]) = 1 < S([1]) = 2$, and the conjectured condition proposes indeed $b^* = [0]$.
Jan
26
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
25
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
25
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
25
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
24
revised Recurrence equation similar to a geometric progression
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Jan
24
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
24
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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Jan
23
revised Choosing the vector that minimizes this sum related to the rearrangement inequality
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