Talk:Random Latin squares: Difference between revisions
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"... generate a random permutation, one row at a time. If a row conflicts with any of the rows above it, generate a new random permutation for that row. The upside is that this is easy to understand and generates uniformly-random Latin squares..."<br>
Does it generate uniformly-random Latin squares? To expose this fallacy let me consider I randomly select 0123 for my first row. Let me first select 1230 with some probability 1/n as my second row. The are now 2 ways to complete this square 2301 as the third row and 3012 as the fourth or 2301 as the fourth row and 3012 as the third. So each of these squares is generated with probability 1/2n, Now again with probability 1/n I select 1032 as my second row. There are now 4 ways to complete this square: 2301 as the third row and
3210 as the fourth; or 3210 as the third row and 2301 as the fourth; or 2310 as the third row and 3201 as the fourth; or 3201 as the third row and 2310 as the fourth. So each of these squares is produced with probability 1/4n.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 19:53, 13 July 2019 (UTC)
:: To the best of my knowledge, it does, in fact, generate uniformly random latin squares. https://www.academia.edu/29890346/Comparison_of_Seven_Techniques_for_Generating_Random_Latin_Squares See page 2. --[[User:Chunes|Chunes]] ([[User talk:Chunes|talk]]) 19:32, 16 July 2019 (UTC)
==Python Algorithm==
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