Talk:Random Latin squares: Difference between revisions
→"restarting row" method: Further comment.
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(→"restarting row" method: Further comment.) |
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::::: Thanks for the correction, both of you. I wonder, did I misinterpret the algorithm as described in the paper, or is the author simply incorrect? Is the "restarting row" method actually more of a "restarting square" method? I will be looking to rewrite my submission as soon as I can wrap my head around an algorithm that works. --[[User:Chunes|Chunes]] ([[User talk:Chunes|talk]]) 16:48, 17 July 2019 (UTC)
:::::: I've had a look at the paper and the author just seems to be wrong about the "restarting row" method producing uniformly random results. In fact the paper seems to be a bit self-contradictory. On the one hand it says in section 1.2:
:::::: "One thing that must be considered in SeqGen methods is that when a conflict is treated, correcting or replacing the repeated symbol can lead to a non-uniform distribution of the generated results."
:::::: On the other hand it says in section 2.1:
:::::: "Also, the generated results are uniformly distributed (if the PRNG used to generate the symbols in the row is not biased)."
:::::: But, as Nigel's example for a Latin square of order 4 clearly shows, what goes in the first two rows is inevitably affecting what goes in the third and fourth rows, not just in the order of the symbols but in the possible number of permutations of those rows and hence the probability distribution of the set of Latin squares being generated is not even approximately uniform. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 19:54, 17 July 2019 (UTC)
:: in particular, you may find this interesting: "The probability of finishing the entire LS is a combination of the previous series of probabilities, but not their product, as the rows are not independent to each other (i.e. row i depends of values on row i-1)." --[[User:Chunes|Chunes]] ([[User talk:Chunes|talk]]) 19:37, 16 July 2019 (UTC)
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