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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 | 2022-06-27 02:54 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <871qvauazi.fsf@bsb.me.uk> (permalink) |
| References | (14 earlier) <7ad01d7a-0352-4efe-b81d-bf6c66bb9e08n@googlegroups.com> <87fsjrt8u5.fsf@bsb.me.uk> <151e87ad-992b-4eaf-bbfa-6a4b6d75759bn@googlegroups.com> <877d52uct3.fsf@bsb.me.uk> <e67dccc3-2c3f-4d9b-ae2a-05eb64b6d1can@googlegroups.com> |
"B.H." <xlt.pjw@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. > 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". > 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? -- 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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