Terminology for a cyclically ordered set of objects If I have an ordered set of objects (for concreteness, say they're integers) $(x_1,\ldots,x_n)$, I might call it a tuple of integers.
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"?
 A: 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. 
A: 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 http://en.wikipedia.org/wiki/Cyclic_order. Its just a certain kind of ternary relation on a set. 
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.
A: 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 $A$".
