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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 | 2022-06-24 21:17 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <87wnd5x1d8.fsf@bsb.me.uk> (permalink) |
| References | (3 earlier) <87mte32dsk.fsf@bsb.me.uk> <e196b3b9-7701-4305-b390-af70f25767e6n@googlegroups.com> <87edzeyhmr.fsf@bsb.me.uk> <03518cd4-79b7-4e68-a680-3c87d4ec14d5n@googlegroups.com> <d3cff16a-d9e1-4cac-a928-5084d8aa3918n@googlegroups.com> |
Paul N <gw7rib@aol.com> writes: > On Friday, June 24, 2022 at 9:00:10 AM UTC+1, malcolm.ar...@gmail.com wrote: >> On Friday, 24 June 2022 at 02:28:34 UTC+1, 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? >> > > 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? >> > >> I had a look at the link and couldn't work out what the problem was. >> Something to do with the product of the signs, but it doesn't actually >> tell you which square is multiplied with which (It can't be simply >> "multiply all squares" as the wording implies, because that's just a >> parity problem.) >> It's understandable that someone would have misunderstood the problem >> if relying on that link. > > I too would be interested to know what the problem is about. I don't > think I have ever heard of the "sign" of a permutation. It's common, when dealing with parity, to make even/odd to 1/-1. That way parities can be combined with multiplication, just as permutations can be factored and multiplied. > If it simply > means whether the permutation can be made up of an odd or even number > of pair switches then the results don't seem consistent with those > given on the page. See my answer to MM on what the problem is about. Do you still see an inconsistency? If so, maybe someone here can help of you explain what you think is inconsistent. -- 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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