# Another name for a discrete set? [closed]

By discrete set, I mean sorting a given number of items into different orders, so that no two sets are alike.

Example, 4 items:

1234
3142
2413
4321


It seems related to a "derangement", but is more specific. So maybe there's a specific term for this, besides "discrete set", which is all I could think of.

EDIT:

Now that I'm looking at latin squares, the following example of a latin square actually repeats sequences between columns (such as 34, 21, 43), whereas my example above does not.

1234
2143
3412
4321


Is my non repeating example a particular kind of latin square or is that not distinguished from other latin squares which repeat sequences?

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Looks like a Latin square to me... –  Douglas S. Stones Oct 21 '10 at 5:45
Cool, thanks; I'll look in to that... –  user10226 Oct 21 '10 at 5:51
I think he means permutations... –  Nick S Oct 21 '10 at 6:53
A Latin square may be thought of as a 2D permutation. Any pair of rows (or any pair of columns) are discordant permutations, and therefore define a derangement. So the OP wasn't that far off (although "discrete set" sounds silly). –  Douglas S. Stones Oct 21 '10 at 9:22
Anyway, you're probably after: row-complete Latin squares (or column-complete Latin squares). See this: designtheory.org/library/encyc/exs/clsex.html –  Douglas S. Stones Oct 21 '10 at 9:24
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## closed as too localized by Andrey Rekalo, Will Jagy, Harald Hanche-Olsen, Captain Oates, Qiaochu YuanOct 21 '10 at 9:17

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