most recent 30 from http://mathoverflow.net 2013-05-24T06:25:44Z http://mathoverflow.net/feeds/question/103146 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103146/terminology-for-a-cyclically-ordered-set-of-objects unknown (google) 2012-07-26T02:20:19Z 2012-07-26T14:25:12Z

<p>If I have an ordered set of objects (for concreteness, say they're integers) $(x_1,\ldots,x_n)$, I might call it a <em>tuple of integers</em>.</p> <p>Perhaps, though, I have an set of integers $(x_1,\ldots,x_n)$ but the order is only defined up to cyclical permutation (imagine they're sitting at distinct points along a circle); so $(x_1,\ldots,x_n)$ is the same as $(x_2,\ldots,x_n,x_1)$. I thus can't call this a "tuple of integers" because that would imply there is a canonical ordering. Is there some standard term I can use, besides the unweildy phrase "cyclically ordered set of integers"?</p>

http://mathoverflow.net/questions/103146/terminology-for-a-cyclically-ordered-set-of-objects/103149#103149 Cheyne H. 2012-07-26T02:56:15Z 2012-07-26T02:56:15Z

<p>It certainly depends on the context. I've seen 'cycle' or 'necklace' used before for this, but you had best define it first as these aren't universal. </p>

http://mathoverflow.net/questions/103146/terminology-for-a-cyclically-ordered-set-of-objects/103189#103189 Lee Mosher 2012-07-26T12:38:56Z 2012-07-26T14:25:12Z

<p>Cyclic orderings are somewhat rare beasts but they do show up here and there. A set with a cyclic ordering is a "cyclically ordered set", just as a set with a total (or partial) ordering is a "totally (or partially) ordered set". The formal definition of a cyclic ordering is found in <a href="http://en.wikipedia.org/wiki/Cyclic_order" rel="nofollow">http://en.wikipedia.org/wiki/Cyclic_order</a>. Its just a certain kind of ternary relation on a set. </p> <p>I suppose if you wanted to mimic "poset" for "partially ordered set" you could say "coset", but I would not advise it :-) and for an exhaustive list of the most common alternatives see the link above.</p>

http://mathoverflow.net/questions/103146/terminology-for-a-cyclically-ordered-set-of-objects/103193#103193 Vladimir Dotsenko 2012-07-26T13:31:45Z 2012-07-26T13:31:45Z

<p>If your objects that sit at distinct points along a circle are all elements of some set $L$, and repetitions are allowed, the term "cyclic words in the alphabet $L$" is fairly commonly used. If no repetitions are allowed, so that you just have an equivalence relation on total orderings of some set $A$, one usually talks about "cyclic orderings of $A$".</p>