504:. Nonnotable concept. The concept would, at first sight, appear to be most of interest in discrete mathematics, in particular for functions on finite domains. But the latter are easily seen to coincide with the bijections. I can't think of any interesting properties (beyond being the generator of a finite cyclic group under composition, which by itself is a somewhat boring observation) that applies to these "cyclic functions" in general, which may go a long way to explaining why we can't find anything about them in the literature under any name. --
722:. For example, one of the google hits refers to the "cyclic function of the kidneys". That has nothing whatsoever to do with the subject of this article. Many other Google and scholar hits are of this kind, or are incidental combinations of the words "cyclic" and "function". So, absent more solid and specific sourcing, I am inclined to vote delete.
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Yes, if it is not covered in any literature we can find, we shouldn't have an article on it. Otherwise we would have articles on all sorts of unremarkable mathematical topics. The general standard is that we should only have an article once there is enough interest in the literature to justify one.
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The issue is that this term seems to be made up by the Art of
Problem Solving site, so pointing to a book by the same author doesn't show much. We had similar issues with MathWorld, which liked to make up terminology not used in the actual literature. If there is no source independent of AoPS that
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Well, there are a bunch of unrelated uses of the term. In many cases, these uses derive from the definitions of the
English words "cyclic" and "function". That is a very poor basis for an article. If there are established "technical definitions" of the term, that requires sources, which I'm not
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as editors above have noted other definitions in sourced literature that should be mentioned. There is clearly no standard definition of the term, but one of an encyclopedia's main uses, especially in technical work, is to be a guide when something is encountered in a publication that doesn't give
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Whatever happens, the current "definition" seems to be somewhat original to me. There are many uses of "cyclic" in the literature, which range from just meaning a function that oscillates, such as sine, to meaning a multivariable function that takes the same value if the variables are shifted in a
681:, as per above: it doesn't seem to be notable, it seems to be the invention of a single person, with no other citations. More seriously though: no examples at all are given, aside from involutions. I can actually think of a pile of additional examples, all well known from the study of
52:. There's a powerful argument here that there's no authoritative source for the use of this term in the math world. We need to be very careful to avoid putting our stamp of approval on things, because then *we* become the authoritative source, whether we like it or not. --
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was recently added by the creator of the article under discussion here. I've never encountered the term in the sense used here, and doubt that it is in significant use for this concept, so I'd be inclined to remove that section. For a very different meaning, see
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293:. My impression is that math and physics folk talk of iterated functions and periodic orbits, whereas computer science folk talk more of cyclic functions. The best content development and context for cyclic functions appears to be in the
689:. So, for this article: no theory is developed: what can one do with 'cyclic functions'? Do they have any interesting properties? Are they applied in any field of study? It sounds like an idiosyncratic invention with no depth to it.
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If the concept lacks a standard name, is that a reason why there should be no article about it? The article need to have some name. This is about functions that generate a finite cyclic group under the operation of composition.
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If the concept lacks a standard name, is that a reason why there should be no article about it? The article need to have some name. This is about functions that generate a finite cyclic group under the operation of composition.
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Given that the original source is AoPS, the right place to look for sources would be in the math competition literature. I have a relevant book or two at home, I will try to remember to see if I can find anything there.
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only refers to the pointwise behaviour of functions, not to that of the iterated function. Take for example the permutation (bijection) on the positive integers whose decomposition in cycles is
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632:, then I would view the article as a neologism, and so I would be in favor of deletion. I did some quick searching, but I could not find a reference apart from AoPS. — Carl
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The notion seems useful, but I don't think the name "cyclic function" is standard. I edited the article slightly but I don't know that it's enough to save it. -
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blog post, a dictionary, and an entire book entitled "Intermediate algebra" also published by AoPS). Such sources alone do not establish notability.
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cyclic fashion. The AoPS source seems problematic, and I hope they do not become the next MathWorld in terms of making up original terminology. — Carl
706:. I'm still not convinced there is a notable topic for an article here. The sources cited in the current article are clearly pretty marginal (an
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The following discussion is an archived debate of the proposed deletion of the article below.
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Non-notable mathematical term. The AoPS source is not reliable because it is a blog.
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That doesn't seem a suitable redirect target to me. What is described at
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Nothing jumps out in those search engine hits as the subject of
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section, so that would seem the best target for a merge. --
348:), ... is a cycle. Yet π is not a cyclic function, since π(
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Iterated function#Abelian property and
Iteration sequences
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281:. This topic occurs in a few different places on WP:
584:Please add new comments below this notice. Thanks,
328:... Let's call it π. Then for any positive integer
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