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 Jan 23 revised Choosing the vector that minimizes this sum related to the rearrangement inequality added 383 characters in body Jan 23 asked Choosing the vector that minimizes this sum related to the rearrangement inequality Jan 21 comment Optimal Strategy for Chosing Lottery Tickets @Lost1: It's not just the distribution. In fact I think (still working it out) that we could formulate it this way: the cost always remains the same, and each time you choose ticket A, the next ticket A will have its probability multiplied by a constant factor $k_A<1$, and ticket B remains the same (and vice-versa). But it might be more or less complicated, I need to think about it a bit more. At any rate, thanks for the answer. Jan 21 comment Optimal Strategy for Chosing Lottery Tickets @Lost1: I understand your concern, but the thing is that I may have been overly liberate with the assumptions. In fact I do know something about future $c$ and $p$, I just thought initially that it did not matter. Obviously, it does. Jan 21 awarded Commentator Jan 21 comment Optimal Strategy for Chosing Lottery Tickets @Lost1,Andrey: good point, it is true that with no information on the subsequent deals, something like this might come up. I probably need to rethink my question. Should I update this post ? Jan 21 accepted Optimal Strategy for Chosing Lottery Tickets Jan 21 revised Optimal Strategy for Chosing Lottery Tickets deleted 1 characters in body Jan 20 asked Optimal Strategy for Chosing Lottery Tickets Dec 3 revised Recurrence equation similar to a geometric progression added 14 characters in body Dec 3 awarded Scholar Dec 3 accepted Why do XOR and other operators on binary variables qualify as linear? Dec 3 comment Why do XOR and other operators on binary variables qualify as linear? Ok I think I got the idea. But so, why are permutations over $\mathbb{F}_2^n$ considered linear ? For instance, consider the data-dependent rotation $Rot(x,y):\mathbb{F}_2^n \times \mathbb{Z}_n \mapsto \mathbb{F}_2^n$ which consists in a circular left shift of $x$ by $y$ positions. Is it linear in $x$ ? Dec 3 comment Why do XOR and other operators on binary variables qualify as linear? @JyrkiLahtonen: Thanks for the comment. I know that XOR is addition mod 2, and this is why I understand it intuitively, but can you give me a mathematical reasonning ? And what do you mean by "takes sums to sums" ? do you refer to the fact that $f(x+y)=f(x)+f(y)$? In this case I don't know how that would translate for binary operators? Dec 3 asked Why do XOR and other operators on binary variables qualify as linear? Jan 31 comment Recurrence equation similar to a geometric progression @leonbloy no, I meant the initial conditions ($T(1) = A$ and $T(n) = B$). Nov 30 comment Distribution probability of elements and pair-wise differences in a sorted list Indeed, thanks for this great answer :-) Nov 30 awarded Supporter Nov 30 comment Distribution probability of elements and pair-wise differences in a sorted list Thanks for the answer! I actually had that after I posted the question, but I was not able to check that $\sum_{i=0}^{N-1} \Pr(x_i = x) = 1$, and somehow started doubting on it. The way you put it makes sense though, and I did that sum numerically which seems to be right! A note on $d$: it seems that $\Pr(d_i = 0) = \frac m {N-m+1} > 0$ which makes no sense if elements are unique... Yet you did take that into account in the pdf of $x_i$. Any idea ? Nov 29 revised Distribution probability of elements and pair-wise differences in a sorted list added 1 characters in body