Suppose I have a set $S$ of $n$ integers picked independently, uniformly at random from $[-L, L].$ Let $z(S)$ be the number of subsets of $S$ which sum to zero. The question is: what is the distributon of the variable $z(S)$ (I am interested in $n$ fixed and $L$ growing)?
$\begingroup$
$\endgroup$
10
asked Jul 5, 2015 at 18:34
-
$\begingroup$ To be clear, you pick $S$ uniformly at random from all size-$n$ subsets of $\{-L, \dots, L\}$, right? (As opposed to picking $n$ integers independently and uniformly at random from $\{-L,\dots,L\}$.) $\endgroup$– usulCommented Jul 5, 2015 at 20:00
-
$\begingroup$ @usul No, actually I mean the entries are picked uniformly, independently, at random (as in your second option). $\endgroup$– Igor RivinCommented Jul 5, 2015 at 20:30
-
1$\begingroup$ @Anthony Quas: I don't think the $x_A$ can be (even approximately) independent, I would expect them to be highly correlated if the two sets have appreciable overlap. $\endgroup$– Christian RemlingCommented Jul 5, 2015 at 21:35
-
1$\begingroup$ @AlexR I am not sure what you are talking about... $\endgroup$– Igor RivinCommented Jul 5, 2015 at 23:55
-
1$\begingroup$ @ChristianRemling Yes, your first comment is correct. $\endgroup$– Igor RivinCommented Jul 6, 2015 at 0:00
|
Show 5 more comments