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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Newsgroups | comp.theory |
| Subject | Re: Resolved: Even vs. Odd Latin Square Problem |
| Date | 2022-06-23 23:52 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <87mte32dsk.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> |
"B.H." <xlt.pjw@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. 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. Making this clear up-front would have been helpful. -- Ben.
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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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