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Jul 25, 2020 at 11:21 comment added Moritz Firsching I updated my question to show non-uniqueness for the case $n=10$, using the clarified definition of the precoloring, I hope I understood correctly now.
Jul 25, 2020 at 11:06 comment added Moritz Firsching ok, so in the example above, $1-2-3-7$ is not the coloring you are looking for? Maybe it would be more clear to remove the sentence "It could also have been $1-2-3-7$?
Jul 25, 2020 at 9:14 comment added vidyarthi @MoritzFirsching I meant that yes, my preference is for the lexicographically smallest order, but, if there are clashes, the the color would be the nearest to that. Suppose, in the coloring I give, I took the string $1-2-3-6$ and not $1-2-3-4$, which was not possible on account of $4$ color in the previous row
Jul 24, 2020 at 18:28 comment added Moritz Firsching I'm unable to grasp the precise definition from "yes, sort of"
Jul 24, 2020 at 14:12 comment added vidyarthi @MoritzFirsching yes, sort of
Jul 24, 2020 at 13:05 comment added Moritz Firsching What pattern exactly for the k-th subdiagonal? Any valid completion for the k-th row? One that starts with 1-2-3-...-k-1? They lexicographically smallest completion?
Jul 24, 2020 at 12:28 comment added vidyarthi @MoritzFirsching edited the post. See now for the pattern I follow
Jul 24, 2020 at 12:27 history edited vidyarthi CC BY-SA 4.0
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Jul 24, 2020 at 12:07 comment added Moritz Firsching At this point, it is still unclear to me, what "follow the same pattern" is. It might help if you clarify what exactly is the precouloring that you are interested in.
Jul 24, 2020 at 10:47 answer added Florian Lehner timeline score: 1
Jul 24, 2020 at 9:53 comment added vidyarthi @FlorianLehner edited the post, thanks
Jul 24, 2020 at 9:53 history edited vidyarthi CC BY-SA 4.0
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Jul 24, 2020 at 9:34 answer added Moritz Firsching timeline score: 1
Jul 24, 2020 at 8:48 comment added Florian Lehner I don't quite understand your description of the pre-coloring. Are there any restrictions on how you colour? For general $n$, shouldn't it be the last $n/2$ subdiagonals?Transversal also has a concise meaning in latin squares, but I don't think this is what you mean by transversal.
Jul 24, 2020 at 6:41 history edited vidyarthi CC BY-SA 4.0
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Jul 22, 2020 at 20:55 history edited vidyarthi CC BY-SA 4.0
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Jul 22, 2020 at 20:13 history asked vidyarthi CC BY-SA 4.0