Talk:Cycle (mathematics)

I agree that the two should be merged. Too much articles on permutations exist and are about exactly the same topic.&mdash; MFH:Talk 19:55, 10 November 2006 (UTC)

I've reverted Merge
I've temporarily reverted the merge of this article into this cyclic permutation, since I'm unconvinced that this is a good idea. I would like to have more discussion about this. Please see the discussion here. Paul August &#9742; 22:31, 18 July 2007 (UTC)

Homology
There should be some kind of cross-reference to cycles in homology. Richard Pinch (talk) 21:47, 30 August 2008 (UTC)

Identifying change
Hm, I see that I forgot to sign in making a change to this page. So I'm 194.167.52.1. Sorry about that, I hope this partially puts it straight.Marc van Leeuwen (talk) 15:50, 13 October 2008 (UTC)

The cycle (0<1).
A cycle is a magnitude of space or of time repeating itself in time. The spectrum of magnitudes starts from Nothingness ‘0’ to the ‘Whole’ of ‘1’ of unlimited magnitude, static from the outside as ‘1’ and dynamic on the inside as (oo). Limited magnitudes ‘c’ are located within (0<c<oo1). Spatial cycle can be a line, an area or a volume. Temporal cycle is dynamic internally and externally. Units of change vary from almost ‘0’ to unlimited magnitude. Velocity of change can approach ‘0’ or it can approach infinity when the change is quantitative. The change can be linear or it can be accelerated. A cycle has one limit which is the centre, where magnitude is minimum, and another limit which encloses the whole of the magnitude of ‘1’. When magnitude of the cycle increases linearly the cycle repeats itself and there is no flowing time. When increase in magnitude is accelerated each added unit is different and growing as 2 to power of 'n' but only when viewed from the beginning of ‘0’. Spatial change of magnitude of a cycle is external because space cannot be within itself. Temporal change of magnitude of a cycle is 1/2 to 'n', it is internal within static ‘1’. Time is contradiction of space. Time is within itself so that magnitude of time is its ‘density’. At each point within the magnitude of the cycle there is a ‘beginning’ ‘0’ and an ‘end’ ‘1’. Magnitude of the cycle (0<1) is always the sum of smaller cycles. A new cycle is transferred from non-existence to existence, or the other way round. The duality of existence non-existence exits only within a limited static cycle ‘c’ located within the unlimited medium of Nothingness (0<c<oo), and only when there is an observer observing from the centre. At the perfect centre the end ‘1’ is identical with the ‘beginning’ ‘0’. At the imperfect centre the end ‘1’ is of magnitude 1/c. Only the accelerated transformation exists and it follows convergent spiral. The outside 2 to 'n' is reflected inside 1/2 to 'n'. Transformation ‘n’ within (0<n<c) can follow any function n=f(n-1). The function controlling all the transformations u-n/c, where (0<i<1), is; n	                       oo   2 i = Σ  u/ n                                 n=1    2

KK (78.146.167.52 (talk) 11:46, 9 May 2010 (UTC)) —Preceding unsigned comment added by 78.146.55.246 (talk)

Reference needed?
I'm puzzled by the "unreferenced" tag. There's something at the bottom of the page that looks to me very much like a reference. Jowa fan (talk) 01:13, 19 April 2011 (UTC) ETA: I'm including this link for my own reference: WP:SCICITE. The section on articles without in-line references would seem to be relevant here. Jowa fan (talk) 01:28, 19 April 2011 (UTC)
 * You're right, it has one reference (which is quite low, the requirement being multiple non-trivial references), but no footnotes. This isn't adequate. Andrevan@ 04:15, 21 April 2011 (UTC) I changed to the single source tag as opposed to unreferenced. Andrevan@ 15:33, 21 April 2011 (UTC)
 * OK, I can look up a second source next week when I'm back at the office (unless someone else fixes this first). Since I'm still learning about the various Wikipedia policies, can you point me to something explaining the multiple references requirement?  The "one source" template points to WP:RS, which doesn't seem to address this issue.  For such a short article, on a topic that many mathematicians would describe as uncontroversial knowledge I wouldn't have expected multiple sources to be necessary. Thanks for any feedback you can offer. Jowa fan (talk) 01:13, 22 April 2011 (UTC)
 * Take a look at Template:Single source, WikiProject Fact and Reference Check/Guidelines, and a discussion at Templates for discussion/Log/2010 May 12. Although a single source is not necessarily a problem, I think it's pretty clear that the referencing on this page is generally poor. I'm not going to go around slapping citation needed tags everywhere, but we can do better than one general reference and 0 inline citations. (The "multiple nontrivial" language was from general notability, which isn't really an argument I meant to make.) Andrevan@ 07:47, 22 April 2011 (UTC)
 * Thanks for the info. Those references don't paint a clear picture on this particular point, but since it's very easy to provide a second source for this material, I've now added one. Overall I don't see the referencing here as being "generally poor": this material is common knowledge for mathematicians, easy to find by scanning the contents page of a relevant textbook, and not in any way controversial, so there's no need to footnote each invididual point.  If this needs any further attention, it should probably wait until after the merger proposal is resolved. Jowa fan (talk) 03:51, 27 April 2011 (UTC)

Merger proposal
I propose the article transposition (mathematics) be merged into this one. Neither article is particularly large or informative, and transpositions are the simplest case of cycles, so their definition and discussion could very well be included here. Also this would make referencing both subjects easier. Marc van Leeuwen (talk) 10:39, 22 April 2011 (UTC)
 * Agreed. Andrevan@ 16:49, 22 April 2011 (UTC)

Order of execution of a product of transpositions
I have two algebra textbooks which indicate that the execution of a product of transpositions proceeds from left to right. If anyone knows of a textbook indicating otherwise, I would like to know what it is so I can look it up. In any case, this article should make clear which transposition in a product, for example (a,b)(a,c) is performed first, (a,b) or (a,c), and cite the source. — Anita5192 (talk) 04:49, 14 May 2013 (UTC)

new merger proposal
Although I didn't make the proposal, I had been thinking about doing so for a while. These pages had been merged back in 2007 for a moment or two, but that merger was reverted (and the merge went the other way, cycle into cyclic permutation). The reason I have hesitated making the proposal is that the title Cycle (mathematics) is much broader than cyclic permutation. Cycles are defined in graph theory, and used in many descriptions of periodic behavior that are not related to permutations, and in several other areas. This article however is exclusively about cyclic permutations. Cycle is already a DAB page and several of the mathematical meanings are listed there, otherwise I would have proposed turning this page into a DAB page. I think that the only reasonable thing to do here is to merge Cyclic permutation into this article and then move this page to Cycle (permutation theory). Bill Cherowitzo (talk) 03:26, 14 June 2014 (UTC)


 * I would have thought to merge Cyclic permutation into Permutation. —Quondum 03:39, 14 June 2014 (UTC)

That is a reasonable suggestion. I didn't put it forward for two reasons. First, it still leaves this page with a bad title (imho) and secondly, the permutation page is starting to get large and I am concerned about it. The permutation page has a wide scope, starting with the very basics and ending up with some sophisticated algorithms for computing permutations efficiently. Packing too much more in there is going to make it hard for readers to get to the information they want. Bill Cherowitzo (talk) 03:58, 14 June 2014 (UTC)


 * Permutation does rather go into applications and methods, which IMO could be split out or dropped entirely. Cyclic permutations and their use in expressing (i.e. from which to compose) finite permutations seem to be more fundamental to the concept than much of the stuff about ordering, generating etc.  And, no offence intended, than the circular permutation concept.  However, your proposal of merging the two articles Cycle (mathematics) and Cyclic permutation into one with a more appropriate name does make sense, which could then be referred to from the Permutation article which would use the concept without elaborating fully on it. This is in keeping with the style in WP. However one arranges it, my major interest would be that at least the definitions are complete and do not sacrifice clarity to a perceived need for pedagogy. —Quondum 05:59, 14 June 2014 (UTC)


 * I agree with the merging of Cyclic permutation and Cycle (mathematics), which both treat the same concept, into one article. The section on counting permutations by number of cycles of Cycles and fixed points could be integrated into this article as well. An alternate title to Cycle (permutation theory) would be Permutation cycle (see MathWorld). Best wishes, --Quartl (talk) 05:27, 1 July 2014 (UTC)