Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was reading a paper that I found via spiked math (

I have problem understanding the subsection Refined permutation and relabelling. Can someone please help?

share|cite|improve this question
It would help if you say what you don't understand. The rearrangement strategy is used before in the paper, trying to reduce the number of configurations that need to be counted. – Ross Millikan Jun 24 '11 at 4:40
I can't see where the "2051 possible B2/B3 pairs" comes from. – Covi Jun 25 '11 at 5:04

The idea is to find assignments to the first three rows of the Sudoku that yield the same number of completed sudokus.

For every assignment of the first three rows, we assign a canonical form by first applying the unique permutation on the digits $1,\ldots,9$ such that the first square is $1,2,3;4,5,6;7,8,9$, then rearranging the other 6 columns in some canonical way (see details in the paper). Canonicalization doesn't change the number of completed sudokus.

Other operations that don't change the number of completed sudokus is permutations of the rows or the columns. The idea is to start with a list of all canonicalized first three rows, and identify items which are related by row/column permutation. You do this by going over all items, applying all possible permutations, and canonicalizing; now you can identify the item you started with with the item you ended with.

share|cite|improve this answer
One thing I don't understand: how does the "2051 possible B2/B3 pairs" come from? – Covi Jun 25 '11 at 4:39
You run the program, and after all equivalent configurations are identified, you are left with 2051 of them. That's an empirical result. – Yuval Filmus Jun 25 '11 at 23:24

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.