Unique Sudokus (Russell & Jarvis)

Everything about Sudoku that doesn't fit in one of the other sections

Re: Unique Sudokus (Russell & Jarvis)

Postby eleven » Sun Jan 21, 2018 9:18 pm

Mathimagics,

i had missed that last post. I knew that with gsf's program/grid collection you can list all automorph puzzle counts (and i told you so).

Thanks for your interesting summary. What i still don't clearly understand is, what happens to the multi-automorphism grids in Red Ed's/Jarvis table.
I think you should find the same grid in different classes, so isn't the sum more than all possible automorph grids ?

Ah, think i got it. This way they just reproduce the multi-automorph count correctly.
eleven
 
Posts: 1738
Joined: 10 February 2008

Re: Unique Sudokus (Russell & Jarvis)

Postby Mathimagics » Sun Jan 21, 2018 10:22 pm

eleven wrote:I knew that with gsf's program/grid collection you can list all automorph puzzle counts (and i told you so).


Surely you have noticed by now that I have to be told some things over and over and over again ... 8-)

eleven wrote:Ah, think i got it. This way they just reproduce the multi-automorph count correctly.


Cool, eh?
User avatar
Mathimagics
2017 Supporter
 
Posts: 547
Joined: 27 May 2015

Re: Unique Sudokus (Russell & Jarvis)

Postby eleven » Sun Jan 21, 2018 10:36 pm

Thanks for your threads. Such i nice way to learn something about group theory.
eleven
 
Posts: 1738
Joined: 10 February 2008

Re: Unique Sudokus (Russell & Jarvis)

Postby JPF » Mon Jan 22, 2018 12:07 am

Hi Mathimagics,

Let's call :
Ne = 5,472,730,538 number of ed Sudoku solution grids
NT = 6,670,903,752,021,072,936,960 exact number of Sudoku solution grids
t = 2 x 6^8 = 362,880 size of the group of geometric transformations


What you call grid deficiency is
Gd = Ne.t.9! - NT = 344,420,270,386,053,120
D = Gd/9! = Ne.t - NT/9! = 949,129,933,824

In Russel & Jarvis' table, Class 1 contains only the identity. Therefore the number of invariants are all the sudoku grids (NT)
Before relabelling, their number is A(1) = NT/9! = 18,383,222,420,692,992

Then D = Ne.t - A(1)

Btw, there is a typo in your table: A(1) = 18,383,222,420,692,992

Yes, gsf calculated the number of automorphisms for each ed sudoku-grid independently of Russel & Jarvis.
The numbers were predicted 2 years before though here
His calculation confirmed both Ne and NT.

and yes, thre are only 560,151 ed sudoku-grids having # automorphisms greater or equal to 2.

JPF

edited a typo
Last edited by JPF on Mon Jan 22, 2018 7:22 am, edited 1 time in total.
JPF
2017 Supporter
 
Posts: 3754
Joined: 06 December 2005
Location: Paris, France

Re: Unique Sudokus (Russell & Jarvis)

Postby Mathimagics » Mon Jan 22, 2018 1:50 am

Thanks JPF!

I fixed the error, that last digit appears to have been lost in transit!

I did notice your handle appearing regularly as I waded through the mire of "About Red Ed's Sudoku Symmetry Group", and "Su-Doku's Maths", etc ..., looking for traces of Red Ed's automorphism enumerator.

Nice of you to chime in with that useful info ...

Cheers!
User avatar
Mathimagics
2017 Supporter
 
Posts: 547
Joined: 27 May 2015

Previous

Return to General