Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.theory > #53092

Re: Resolved: Even vs. Odd Latin Square Problem

Show all headers | View raw

"B.H." <xlt.pjw@gmail.com> writes:

> On Sunday, June 26, 2022 at 9:54:44 PM UTC-4, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes: 
>> 
>> > On Sunday, June 26, 2022 at 9:15:22 PM UTC-4, Ben Bacarisse wrote: 
>> >> "B.H." <xlt...@gmail.com> writes: 
>> >> 
>> >> > On Sunday, June 26, 2022 at 5:26:29 PM UTC-4, Ben Bacarisse wrote: 
>> >> >> "B.H." <xlt...@gmail.com> writes: 
>> >> >> 
>> >> >> > On Sunday, June 26, 2022 at 9:44:07 AM UTC-4, Ben Bacarisse wrote: 
>> >> >> 
>> >> >> >> You were wrong about having resolved the open problem you posted about. 
>> >> >> >> It's still open. You don't appear to have changed you mind about that. 
>> >> >> > 
>> >> >> > I am not wrong at all, it is surprising that you claim to think that 
>> >> >> > that easy proof, which I will not publish, does not exist. 
>> >> >> There are counterexamples. There can be no proof that (in your words) 
>> >> >> "it is actually the case that for every positive integer m, the number 
>> >> >> of even Latin squares of order m and the number of odd Latin squares 
>> >> >> of order m are *the same*" 
>> >> >> because there is (to take just one counterexample) no odd 1x1 Latin 
>> >> >> square. When I asked about this you said 
>> >> >> "The odd Latin square of order 1 is simply the square with one cell 
>> >> >> containing -1" 
>> >> >> but that is an even Latin square. 
>> >> > 
>> >> > You finally stated your objection. 
>> >> 
>> >> There are two: that the Latin square you gave is even, and that there 
>> >> are counterexamples (included in the page you linked to) to your claimed 
>> >> resolution. 
>> >> > 
>> >> > "A latin square is even if the product of the signs of all of the row 
>> >> > and column permutations is 1 and is odd otherwise. " 
>> >> 
>> >> Yes, so your example is an even Latin square, not an odd one. Unless 
>> >> there is (up to isomorphism) exactly one odd Latin square the simple 
>> >> case of n=1 is a counterexample to your claimed resolution. The page 
>> >> you linked to included 7 other counterexamples -- basically every known 
>> >> case is a counterexample. 
>> >> 
>> >> > If you treat the same square as the selected row and column, then the 
>> >> > "base case" would have to be changed to a 2 x 2 Latin square, where it 
>> >> > would work. 
>> >> > 
>> >> > I am not sharing the rest of the details of the proof with you. 
>> >> 
>> >> There can't be a proof of your claim because there are counterexamples. 
>> >> They were even listed in the page you linked to. 
>> >
>> > I don't know what table you have called master and bowed humbly to, 
>> > but you are incorrect. I am familiar with the mathematical proof, and 
>> > your insistently repeated protestations to the contrary are patently 
>> > incorrect.
>> All identity permutations are even. Every 1x1 Latin square has 1 even 
>> row permutation (the identity permutation) and one even column 
>> permutation (the same). Every 1x1 Latin square is even. There are no 
>> odd 1x1 Latin squares.
>
> If you re-define permutations in a way that is consistent with non-1x1
> Latin squares,

And, apparently, you have redefined the very notion of counting Latin
squares since you believe there are at least two 1x1 Latin squares.

So you redefined how you count the squares, and you redefined what even
and odd squares are and you proved something about these new counts.
That unseen proof can't be about the conjecture you linked to because
that conjecture counts equivalence classes of squares so that the actual
n symbols used don't matter.

> the conjecture is provably true.

Some other, as yet unstated, conjecture is provably true.  You would
need to state, at least, how you counting Latin squares since you count
more 1c1 squares than anyone else.

The conjecture you linked to can not be resolved in the way you claimed
(all the counts being the same) because there are counterexamples.

> If you don't re-define them, the conjecture I stated is true based on
> the 2 x 2 Latin square.

Quite possibly.  I am only talking about the claim to have resolved the
conjecture you linked to.

> You are emphasizing the wrong point so you
> can say something that is true.

Unfortunately that is in the very nature of pointing out an error.  I
could go look for some true things you've said, but I don't even know
how you are counting squares (you never said) so I would have to guess
what you say you have proved.

>> > You ignored my idea about a different permutation definition for the 1 
>> > x 1 matrix--where -1 is an odd Latin square because there is only one 
>> > permutation in this case, and the product, "-1" is taken to be -1 
>> > making it odd.
>> You claimed to have resolved the conjecture you linked to, not one based 
>> on your own notion of what's odd and what's even. I can resolve the 
>> twin prime conjecture, provided you accept my alternative definition of 
>> "prime" and "twin".
>
> I did, it follows from my own claim.  There are different
> interpretations of the imprecisely phrased conjecture.  The conjecture
> is resolved, I proved it.

You should have know that you were not addressing the open problem given
in the link, since that page clearly shows that there is only one 1x1
Latin square.  Since your notion of counting differs from that used to
state the conjecture, how could you think you had resolved it?

But, in fact, there is nothing imprecise about the conjecture.  You
didn't know what some of the terms meant (even and odd Latin squares,
how to count distinct squares), but guessing does not mean the wording
was imprecise.  Not all conjectures are explained in the most basic
terms.  For some, you have to know how the "terms of art" are defined.

>> > Your debating style and efforts to kill me with false claims about 
>> > math anger me, as you can see.
>>
>> I am not trying to kill you. If you feel threatened I will, of course, 
>> stop replying. Do you feel safe enough to continue this exchange?  
>
> I think you are, though not overtly.

That's a shocking thing to say.

> I think you should stop replying;

OK.  I read this only after typing the above, so I'll send it but you
won't hear anything more from me on this topic.  Would you rather I
don't reply to any of your technical posts?  I am very happy to refrain.
I have no desire to cause you any distress.

-- 
Ben.

Back to comp.theory | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

Resolved:  Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-22 10:40 -0700
  Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-22 10:42 -0700
    Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-22 10:50 -0700
  Re: Resolved:  Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-22 19:25 +0100
    Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-23 07:03 -0700
      Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-23 23:52 +0100
        Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-23 16:07 -0700
          Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-24 02:28 +0100
            Re: Resolved: Even vs. Odd Latin Square Problem Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-06-24 01:00 -0700
              Re: Resolved: Even vs. Odd Latin Square Problem Paul N <gw7rib@aol.com> - 2022-06-24 04:50 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-24 08:38 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-24 21:38 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-24 14:04 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Jeff Barnett <jbb@notatt.com> - 2022-06-24 23:06 -0600
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-25 07:22 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Jeff Barnett <jbb@notatt.com> - 2022-06-25 11:25 -0600
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-25 14:06 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Jeff Barnett <jbb@notatt.com> - 2022-06-25 16:40 -0600
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-25 17:21 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-26 01:02 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-25 17:26 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-26 14:44 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-26 07:47 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-26 22:26 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-26 17:57 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-27 02:15 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-26 18:27 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-27 02:54 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-27 08:51 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-27 21:56 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-27 15:56 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-26 08:03 -0700
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-26 21:49 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-24 21:17 +0100
                Re: Resolved: Even vs. Odd Latin Square Problem Paul N <gw7rib@aol.com> - 2022-06-25 04:44 -0700
              Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-24 21:14 +0100
            Re: Resolved: Even vs. Odd Latin Square Problem "B.H." <xlt.pjw@gmail.com> - 2022-06-24 08:35 -0700
              Re: Resolved: Even vs. Odd Latin Square Problem Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-06-24 21:30 +0100

csiph-web