Re: Resolved: Even vs. Odd Latin Square Problem

From	Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups	comp.theory
Subject	Re: Resolved: Even vs. Odd Latin Square Problem
Date	2022-06-24 21:30 +0100
Organization	A noiseless patient Spider
Message-ID	<87r13dx0s4.fsf@bsb.me.uk> (permalink)
References	(2 earlier) <8f294a79-0d74-4f3b-8f6f-7e99d19993ecn@googlegroups.com> <87mte32dsk.fsf@bsb.me.uk> <e196b3b9-7701-4305-b390-af70f25767e6n@googlegroups.com> <87edzeyhmr.fsf@bsb.me.uk> <12d37df2-f9b9-48cb-931d-abb32828ed8cn@googlegroups.com>

Show all headers | View raw

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

> On Thursday, June 23, 2022 at 9:28:34 PM UTC-4, Ben Bacarisse wrote:
>> "B.H." <xlt...@gmail.com> writes: 
>> 
>> > On Thursday, June 23, 2022 at 6:52:30 PM UTC-4, Ben Bacarisse wrote: 
>> >> "B.H." <xlt...@gmail.com> writes: 
>> >> 
>> >> > On Wednesday, June 22, 2022 at 2:25:32 PM UTC-4, Ben Bacarisse wrote: 
>> >> >> "B.H." <xlt...@gmail.com> writes: 
>> >> >> 
>> >> >> > Hi everyone, 
>> >> >> > 
>> >> >> > I just found an easy proof that the answer to this problem: 
>> >> >> > 
>> >> >> > http://www.openproblemgarden.org/op/even_vs_odd_latin_squares 
>> >> >> > 
>> >> >> > ...is that the conjecture is false, assuming I understand it correctly. 
>> >> >> > 
>> >> >> > According to my understanding, 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*. 
>> >> >> There is one even latin square of order 1. What is the odd latin square 
>> >> >> of order one? How could there possibly be such a thing? 
>> >> >> 
>> >> >> The number of even and odd latin squares is known for small n and they 
>> >> >> are (so far) all different. 
>> >> >> 
>> >> > 
>> >> > Since there are infinitely many integers, I decided to count Latin 
>> >> > squares by sign. That is, each Latin square cell is either a "1" if 
>> >> > its sign is negative, or a "0" if its sign is positive. 
>> >> > 
>> >> > The odd Latin square of order 1 is simply the square with one cell 
>> >> > containing -1. 
>> >> > 
>> >> > I resolved the conjecture 
>> >> So you were addressing some other conjecture of your own. 
>> > 
>> > It's close enough.
>> For what?
>
> It is close enough to provide a clear solution to whatever conjecture you likely think it is.
>
>> > The same proof logic resolves all versions of the conjecture, and the 
>> > purpose is to understand the logic of the proof and what it can imply, 
>> > not just to understand one single fact about Latin squares.
>> The version in the link you posted remains an open problem.
>
> I disagree.

So far there is no proof one way or the other.  That makes it an open
problem.

What you posted about before was about another problem (which may or not
have been open at the time) based on what you interpreted even/odd as
meaning for Latin squares.  It had to be about another problem, because
the number of even and odd Latin squares is know for small n.

> The proof is useless, I might publish it if you would agree to
> acknowledge that it is correct and not just auto-smear me.

I did not intend to smear you, automatically or otherwise.

And I have no wish to add to your worries.  I will happily not read what
you write if that would be preferable for you.  Please let me know.

>> You announced a solution without knowing what even and odd mean in the 
>> context of Latin squares? 
>
> I don't have time to read academic papers, I'm not being paid.  I read
> the definitions on OPG and Wikipedia.
>
> Do you know what they are?  I stated my understanding, why do you
> think it's I who have some serious explaining to do, Dr. Bacarisse?

I have posted a reply to Malcolm with what I think is the correct
meaning for odd and even in the context of Latin squares.  (I do not
have a PhD -- I am plain Mr -- but I prefer the more chatty Ben).

-- 
Ben.

Back to comp.theory | Previous | Next — Previous 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