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 02:28 +0100
Organization	A noiseless patient Spider
Message-ID	<87edzeyhmr.fsf@bsb.me.uk> (permalink)
References	<fa1cd8ee-5be5-4ad4-8a46-240b0054dbcbn@googlegroups.com> <87y1xo3691.fsf@bsb.me.uk> <8f294a79-0d74-4f3b-8f6f-7e99d19993ecn@googlegroups.com> <87mte32dsk.fsf@bsb.me.uk> <e196b3b9-7701-4305-b390-af70f25767e6n@googlegroups.com>

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"B.H." <xlt.pjw@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?

> 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.

>> If the terms 
>> used in the page you linked to have their usual meanings, it's clear 
>> that the number of even Latin squares of order m and the number of odd 
>> Latin squares of order m can not possibly be the same. 
>
> What are the usual meanings?  The terms are vague.  Whether or not you
> have a math degree, you might want to clarify yourself.

You announced a solution without knowing what even and odd mean in the
context of Latin squares?

-- 
Ben.

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

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