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Oct 7, 2019 at 19:28 comment added vidyarthi @bof thanks for that observation. Edited the question now.
Oct 7, 2019 at 19:27 history edited vidyarthi CC BY-SA 4.0
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Oct 7, 2019 at 3:42 comment added bof I don't understand the statement. What does your conjecture say in the special case where $m=n$? It's not the Dinitz Conjecture because the DC does not require distinct symbold on the diagonal, and I believe it would be false if you just added that requirement. Also not sure what "fill a maximum of $\min(m,n)$ symbols . . ." means. If it means "fill at most $\min(m,n)$ symbols," can't you satisfy it trivially by leaving all cells empty?
Sep 13, 2019 at 11:55 comment added vidyarthi @RebeccaJ.Stones yes, the latin rectangle is partial, that is, has some empty cells
Sep 7, 2019 at 14:37 history asked vidyarthi CC BY-SA 4.0