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Commits on Jun 26, 2015
Commits on Jun 25, 2015
  1. raneys: minor work on lemma 9 pf.

    committed
    I just realized I have a serious problem with my current proof. It's serious
    enough that the entire lemma may be false. I'm going to have to think about
    this.
Commits on Jun 24, 2015
  1. raneys: work on lemma 9 pf.

    committed
Commits on Jun 23, 2015
  1. raneys: start pf of lemma 9, add g_k outline img.

    committed
    I found it challenging to get the image close to a quality level I'm
    ok with. I wish I knew how to set it up entirely as a vector-based
    image. I also wish I knew how to exclude the figure caption in the pdf
    output; in that case I'd have excluded the caption entirely in both
    output formats.
  2. raneys: add todo item so I don't forget it.

    committed
    This could have been a github issue, but focusing on this one file is my
    current workflow, so this makes more sense to me in this special case.
Commits on Jun 22, 2015
Commits on Jun 20, 2015
  1. raneys: add statement of Pr sum-pos for rand x.

    committed
    Next up I would like to renumber the results to be more consistent. The
    claim will be numbered, and I'll probably rename it to a lemma.
Commits on Jun 17, 2015
  1. raneys: add theoretical rnd x value of E sigma(x).

    committed
    Specifically, this is what I came up with today, for length-n x:
    E sigma(x) = n * (2n-1)!! / (2n)!!
    This is a value that strictly increases without bound, albeit slowly.
    
    I'm afraid it may take some time for me to write this part up nicely.
    My current proof is much more involved than any of the previous proofs
    in the notes.
Commits on Jun 16, 2015
  1. raneys: add code to explore sigma of rand x seq.

    committed
    As opposed to rand s seq.
Commits on Jun 15, 2015
  1. raneys: update sigma(x) to work on all valid seqs.

    committed
    What's new is that sigma(x) will now work properly on sequences that
    need to be shifted, as in they aren't given in a sum-positive order, but
    do have a positive total sum.
Commits on Jun 14, 2015
Commits on Jun 13, 2015
  1. raneys: rm old section 3 text, add lua test code.

    committed
    The new Lua code empirically checks property 7. So far, the results look
    good.
Commits on Jun 12, 2015
Commits on Jun 11, 2015
Commits on Jun 10, 2015
Commits on Jun 9, 2015
Commits on Jun 8, 2015
  1. raneys: finish proof on unif rand perms.

    committed
    I realize this is a small proof to a relatively easy fact. I may
    consider moving it out into prose.
Commits on Jun 7, 2015
Commits on Jun 6, 2015
Commits on Jun 5, 2015
  1. raneys: rewrite sect 3 intro to random sequences.

    committed
    This resets the context in which we'll work there.
Commits on Jun 4, 2015
  1. raneys: minor tweaks to Lua script.

    committed
    I checked out a discrete version; qualitative behavior looks similar,
    but not identical, to the continuous case.
Commits on Jun 3, 2015
  1. Add raneys.lua to empirically test ideas.

    committed
    It turns out my assumptions were waaay off with respect to the
    distribution of permutations of partial sums of a sequence of uniformly
    random values. I'm a surprised and intrigued by what I see here.
  2. raneys: realize smth I thought was true is false.

    committed
    I'll have to reconsider how I'm doing things in the final section.
    
    It may be a good idea to write my code now that empirically checks
    things.
Commits on Jun 1, 2015
Commits on May 31, 2015
Commits on May 30, 2015
Commits on May 29, 2015
Commits on May 28, 2015
Commits on May 27, 2015
Commits on May 26, 2015
  1. raneys: complete pf of new property 5.

    committed
    This proof ended up being more complicated than I wanted it to. I wonder
    if there's a way to clarify and simplify it.
Commits on May 25, 2015
  1. raneys: start writing up bounds on int sequences.

    committed
    Starting with this commit, property 5 will be about bounds, and what I
    previously called property 5 will soon be renamed property 6 or possibly
    another number. Sadly, my current manual numbering system is suboptimal
    and something I hope I can improve on within my system.
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