"A treasure captured! The "Necklace" subset of orthogonal diagonal Latin squares has been found!"

Message boards : News : "A treasure captured! The "Necklace" subset of orthogonal diagonal Latin squares has been found!"

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hoarfrost
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Message 259 - Posted: 22 Dec 2017, 20:57:05 UTC

Early morning of 15 December 2017 with 2 hours and 22 minutes difference, project server received two results for workunit R9_000478253 - from damotbe (L'Alliance Francophone) and Bryan (SETI.USA). Both files are identical (as it must be for correct results) and contain an 8 squares. Many of computation results contain 8 and even more squares, but is this case only first two of them corresponds to usual pair of ODLS, but other 6 squares... were mutually orthogonal! (And, of course, all of this squares were constructed by rows permutation!)

We get a first of squares from this MODLS set and found all (not only "permutation") orthogonal diagonal Latin squares for it, then - all ODLS for "root square" and the squares, found on the previous step, and repeat this process until while we were given a new squares. The results of this search you can see in figure below.


Squares, presented in this graph as nodes and edges denote an orthogonal relationship between squares, lined up into astonishing, symmetrical figure! The core of it is fastened by six MODLS, which are broken into three groups. Each group (originating from two squares) is the basis for four-level branch constructed from 14 squares.

If you are interested in this, you can download this set of 48 squares.
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damotbe

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Message 261 - Posted: 23 Dec 2017, 8:05:07 UTC - in response to Message 259.  

I don't understand the maths behind that, but you feel very enthousiast about this.
It's beautiful ! I'm happy to help you in your research. :-)
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Profile Bryan

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Message 262 - Posted: 23 Dec 2017, 13:26:07 UTC - in response to Message 261.  

I don't understand the maths behind that, but you feel very enthousiast about this.
It's beautiful ! I'm happy to help you in your research. :-)


And you and I will finally get a ODLS Pairs found badge :)

I'm also happy to be helping the project.
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Profile Natalia
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Message 263 - Posted: 23 Dec 2017, 19:37:45 UTC

The badges for ODLS found have been assigned! :)
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Profile Bryan

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Message 264 - Posted: 23 Dec 2017, 20:26:58 UTC - in response to Message 263.  

I was joking, but thank you :)
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hoarfrost
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Message 265 - Posted: 23 Dec 2017, 20:34:06 UTC

In terminology of adventure novels by Stevenson, top crunchers of our project are great crunch-pirates!
With fleets of light destroyers (like damotbe) and individual great battleships (like Daniel).

Great thanks for all crunchers of project!
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Message boards : News : "A treasure captured! The "Necklace" subset of orthogonal diagonal Latin squares has been found!"


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