Okay, that's a plausible hypothesis. (Btw, I sent a strikethrough across the first "is" — which I guess is not ASCII.) Now to answer that we should come up with at least one concrete definition of "a random relation". So we need a positive probability distribution on Z^26. An easy one is this: For any subset X of Z^26, let Prob(X) := Sum_{x in X} rho(cube(x)) , where cube(x) is the unit cube centered at x and aligned with the axes, and rho is the probability (defined on Borel subsets of R^26) given by the standard normal distribution on R^26. (Or, choose your scale factor to taste.) —Dan
On Sep 25, 2015, at 3:55 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I was leaving the definition of "overwhelmingly" up to anyone who knew any results. My intuition is that there is a "phase change" phenomenon, where below a certain critical threshhold almost no groups collapse, while above it almost all do; if that is true, then the position of the halfway point will answer my question. But anything about this general question will interest me.
On Fri, Sep 25, 2015 at 6:52 PM, Dan Asimov <asimov@msri.org> wrote:
That depends on what the definition of is overwhelmingly is.
—Dan
So I think we still need F, R, and V
Andy.Latto@pobox.com
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On Sep 25, 2015, at 3:48 PM, Allan Wechsler <acwacw@gmail.com> wrote:
I would love to see some results on how many random relations (of some distribution of length) you have to throw at an n-generator free group before it becomes overwhelmingly likely that the group is (a) finite, (b) trivial.
On Fri, Sep 25, 2015 at 6:09 PM, Andy Latto <andy.latto@pobox.com> wrote:
On Fri, Sep 25, 2015 at 5:51 PM, Warren D Smith <warren.wds@gmail.com> wrote:
WRAP=RAP so R=1 ,
This shows W = 1, but doesn't help us with R.
PASS=PAS so S=1,
PAS isn't a homonym of PASS. Fortunately, it's a homonym of PA, so this still gives is S = 1.
WHAT=WATT hence T=1,
I think WHAT rhymes with NUT, while WATT rhymes with NOT, so these are not homonyms, at least in my dialect.
But BUT = BUTT gives T=1.
I don't see an F in your list, but RUFF = ROUGH at least gives us F^2 =
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