Essentially different grids & group theory.

Programs which generate, solve, and analyze Sudoku puzzles

Essentially different grids & group theory.

Postby MartinCHarvey » Sun Mar 14, 2021 7:58 pm

Many thanks for previous assistance in this group. I get up to 12199113 isomorphisms with 11 givens, at which point, a small refactor to use less ram is necessary.

Save myself the computation time and disk space, is there a "Group theory for dummies" * textbook which I might find useful?

MH.

* Dummies = BSc math, but not a PhD ...
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Re: Essentially different grids & group theory.

Postby Serg » Mon Mar 15, 2021 7:35 am

Hi, MartinCHarvey!
MartinCHarvey wrote:I get up to 12199113 isomorphisms with 11 givens, at which point, a small refactor to use less ram is necessary.
Save myself the computation time and disk space, is there a "Group theory for dummies" textbook which I might find useful?

Please, use more precise terminology. "Isomorphism" is some kind of transformation. But it seems you say about number of transformed objects (grids, puzzles, etc.). It looks like you are saying about essentially different patterns (9 x 9 binary matrices, where ones mark clue cells of 9 x 9 Sudoku puzzle).

Saying about textbook - I like textbook "An Introduction to the Theory of Groups" by Joseph J. Rotman (Springer series "Graduate Texts in Mathematics"). You should read chapters 1-3 only. Key theoretical concept - "Burnside's Lemma" (you can find it in Wikipedia too).

Serg
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Re: Essentially different grids & group theory.

Postby MartinCHarvey » Mon Mar 15, 2021 2:12 pm

Serg wrote:Hi, MartinCHarvey!
Please, use more precise terminology.


Sorry, I'll learn the terminology and be more precise in future!

Serg wrote:"An Introduction to the Theory of Groups" by Joseph J. Rotman


Thank you, ordered, and I'll work my way through it.

MH.
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Re: Essentially different grids & group theory.

Postby coloin » Wed Mar 17, 2021 6:40 pm

from number-of-non-equivalent-patterns-having-n-clues
Code: Select all
 0   1
 1   1
 2   5
 3   21
 4   109
 5   548
 6   3074
 7   16847
 8   92393
 9   489448
 10  2499689
 11  12199113
 12  56737622
 13  250632745
 14  1049547176
 15  4159131734
 16  15578997961
 17  55113078988
 18  184060159680
 19  580219975879
 20  1726649409444


Yes as Serg says It appears that you are counting patterns .....

If your patterns also had numbers ... they could be termed subpuzzles ... [having multiple solutions so not quite puzzles]...

A grid is a very loose term but the term solution grid is a better one - as in a complete 9*9 solution grid.
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