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The proof of 5472730538 essentially different Sudoku grids

 
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matcos

Joined: 21 Apr 2007
Posts: 1
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Location: the Netherlands

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PostPosted: Sat Apr 21, 2007 7:44 pm    Post subject: The proof of 5472730538 essentially different Sudoku grids Reply with quote

Hello,

I looked on Frazer Jarvis's site, (sudgroup.html) and tried to check the proof. One of the things I would like to do is find Sudoku-grids which is invariant for each of (one representant of) the classes as defined on this site. I can't find a Sudoku-grid which is invariant under class 134, however there must be a lot of them!

The described member of class 134 is of order 2 and it has 9 fixpoints, all in the first 3 rows (in the notation of Ed Russell and Frazer Jarvis no 1,5,9, 10,14,18, 19,23,27).

Could someone give me a clue?

--MatCos
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coloin

Joined: 05 May 2005
Posts: 97
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PostPosted: Tue Apr 24, 2007 12:48 pm    Post subject: Reply with quote

You might be interested in this canonical form thread.....

gsf has a file with all the grids - minlex

Here is a published sample of the grids with >26 automorphisms - Possibly the one you want is there !
Code:
here are the 27 and up grids with #automorphisms, band, and minlex index.
123456789456789123789123456231564897564897231897231564312645978645978312978312645 # 648 001 964550
123456789456789123789123456231564897564897231897231564312978645645312978978645312 # 108 001 964558
123456789456789123789123456231564897564897231897231564348672915672915348915348672 # 54 001 964568
123456789456789123789123456231564897564897231897231564348915672672348915915672348 # 54 001 964569
123456789456789123789123456231564897564897231978312645312645978645978312897231564 # 36 001 964589
123456789456789123789123456231564978564897312897231645312978564645312897978645231 # 72 001 965096
123456789456789123789123456231564978564978231978231564312645897645897312897312645 # 108 001 965174
123456789456789123789123456231564978564978231978231564312897645645312897897645312 # 36 001 965182
123456789456789123789123456231564978645897231897312564312645897564978312978231645 # 36 001 966422
123456789456789123789123456231597864597864231864231597312678945678945312945312678 # 36 001 985543
123456789456789123789123456231597864597864231864231597312948675675312948948675312 # 36 001 985544
123456789456789123789123456231678945678945231945231678312597864597864312864312597 # 36 001 989378
123456789456789123789123456231678945678945231945231678312894567567312894894567312 # 36 001 989379
123456789456789123789123456231897564564231897897564231348672915672915348915348672 # 27 001 989400
123456789456789123789123456231897564564231897978645312312978645645312978897564231 # 36 001 989404
123456789456789123789123456231897645564312897978564231312978564645231978897645312 # 36 001 989622
123456789456789123789123456234567891567891234891234567318642975642975318975318642 # 54 001 992761
123456789456789123789123456234567891567891234891234567345678912678912345912345678 # 54 001 992769
123456789456789123789123456234567891567891234891234567372615948615948372948372615 # 54 001 992773
123456789456789123789123456235964817817235964964817235392641578578392641641578392 # 54 001 1006748
123456789456789123789123456267591348591834672834267915375618294618942537942375861 # 54 001 1007164
123456789456789123789123456267591834591834267834267591375618942618942375942375618 # 162 001 1007168
123456789456789123789123456267591834591834267834267591375942618618375942942618375 # 54 001 1007169
123456789456789123789132465231564978564978231978213546312645897645897312897321654 # 36 004 50092115
123456789456789123798132465231564897564897231879213546312645978645978312987321654 # 36 009 224283635
123456789456789123897231564231564978564978231789312645312645897645897312978123456 # 54 016 473714886
123456789456789231789123645231564897564897312897231456375618924618942573942375168 # 36 027 1012364857
123456789456789231789123645231564978564897123897231564375942816618375492942618357 # 36 027 1012366524
123456789456789231789312456231564978564978312978123564312645897645897123897231645 # 27 030 1061944621
123456789456789231789312456231645978645978312978123645312564897564897123897231564 # 54 030 1062073983
123456789457189236968372514291738465374265198685941327546813972732694851819527643 # 36 133 4869572229
123456789457189326869372514214965873635847192978213465381624957546798231792531648 # 36 240 5449015463
123456789457289163689173452235964817816735924974812635392641578568397241741528396 # 54 348 5472677656
123456789457289163689173452245968317316745928978312645564897231731524896892631574 # 108 348 5472677695
123456789457893612986217354274538196531964827698721435342685971715349268869172543 # 72 416 5472730538


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