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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 2022-06-22 19:25 +0100
Organization A noiseless patient Spider
Message-ID <87y1xo3691.fsf@bsb.me.uk> (permalink)
References <fa1cd8ee-5be5-4ad4-8a46-240b0054dbcbn@googlegroups.com>

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

-- 
Ben.

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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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