I feel that Warren and I are speaking past each other. Can someone (other than Warren or myself) who thinks he/she understands both what I am trying to say and what Warren is trying to say comment on our mutual incomprehension? (Is Warren saying that, contrary to my assertion, the event "there exists an ordering such that x_j<j/N for each j=1,2,3,...,N" IS indeed the conjunction of the N events of the form "there exists an ordering such that x_j<j/N" with j varying over 1,2,3,...,N? Or is he saying that my assertion is correct but irrelevant to his point?) Jim Propp On Tue, Nov 11, 2014 at 2:14 PM, Warren D Smith <warren.wds@gmail.com> wrote:
1. The OEIS strikes again! A conjectured closed form is now found from A124774 which is explained on the web page http://rangevoting.org/CombinedTestFail.html along with everything else I found out, which page I strongly suggest math-funners read, since they seem to keep not comprehending the problem, and maybe this page un-mysterifies. (I'm actually boggled at how much everybody cannot understand the problem, which proves it must be a great problem, and/or I am crazy.)
2. To answer James Propp
I do not understand Warren's example. Specifically, I do not know what he has in mind as the independent events whose conjunction is being considered.
Note that the event "there exists an ordering such that x_j<j/N for each j=1,2,3,...,N" is not the conjunction of the N events "there exists an ordering such that x_1<1/N", "there exists an ordering such that x_2<2/N", ..., "there exists an ordering such that x_N<N/N".
--No....: All N! orderings such as x1,x2,xN, and x2,x1,...,xN, and ... xN...x2,x1 are considered. What is the freaking chance, that at least one of these orderings obeys (after reordering) xj<j/N for each j=1,2,3,...,N? [Where each x_j is an iid uniform(0,1)]
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