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There are a lot of questions concerning cyclic sums, but I just noticed there is no tag for these sums, and it hasn't been suggested as far as I can tell.

  • There are a lot of questions involving cyclic sums.

  • Commonly used relevant tags include , , , and .

  • I think cyclic sums are a distinct enough thing to have apart from the above common tags.

Martin Sleziak has also pointed out that symmetric sums are fairly similar and should probably fall under the same tag. So perhaps something like a would be good. Another common tag relevant here is .

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    $\begingroup$ It seems that at least in some cases the tag (symmetric-polynomials) is used. For example, if you have a look at the posts tagged symmetric-polynomials+summation and symmetric-polynomials+inequality. If tagging of questions about cyclic sums is discussed, probably we should look at symmetric sums... $\endgroup$
    – Martin Sleziak
    May 10, 2019 at 4:32
  • $\begingroup$ ...at the same time. (The two notions appear sometimes in the same problem. Both types of sums often appear in contest math problem.) $\endgroup$
    – Martin Sleziak
    May 10, 2019 at 4:33
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    $\begingroup$ Specifically, I want to ask whether it might be better to have only one tag for both types of sum - cyclic and symmetric. (So that we do not end up with too many too specific tags. As you've mentioned, very often the question will have also (contest-math) tag. There are certainly many question which in addition would have (cyclic-sum) and (inequality) - which means already three spots for tags out of five.) $\endgroup$
    – Martin Sleziak
    May 10, 2019 at 4:36
  • $\begingroup$ FYI, you can make a suggestion on Tag Management 2019 $\endgroup$
    – YuiTo Cheng
    May 10, 2019 at 5:46
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    $\begingroup$ "I think cyclic sums are a distinct enough " maybe you could elaborate on this. What is the common mathematical substance of the questions that should be tagged like this? Is there somebody that might consider themselves as an expert on cyclic sums? $\endgroup$
    – quid Mod
    May 10, 2019 at 7:14
  • $\begingroup$ Good idea as usual @MartinSleziak $\endgroup$
    – Simply Beautiful Art
    May 10, 2019 at 11:49
  • $\begingroup$ @quid I would say I am fairly decent at tackling most sum problems, yet I'd also say I cannot tackle most cyclic sum problems. As for a specific user, I know Michael Rozenburg often answers such questions. At this moment, 4/10 of his newest posts are relevant. $\endgroup$
    – Simply Beautiful Art
    May 10, 2019 at 11:55
  • $\begingroup$ @YuiToCheng Thanks :) $\endgroup$
    – Simply Beautiful Art
    May 10, 2019 at 11:55
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    $\begingroup$ If (cyclic-sum) is going to be created, Michael Rozenburg is going to earn a new gold badge :) $\endgroup$
    – YuiTo Cheng
    May 10, 2019 at 12:09
  • $\begingroup$ I still don't see an answer to the question what the common mathematical substance would be. $\endgroup$
    – quid Mod
    May 10, 2019 at 14:28
  • $\begingroup$ @quid Oh my bad, missed that question. Not entirely sure what you mean, I imagine anything involving cyclic/symmetric sums? $\endgroup$
    – Simply Beautiful Art
    May 10, 2019 at 14:29

1 Answer 1

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I am posting an answer regarding this specific aspect, so that it's easier to comment (and vote) on this specific issue. (Basically summarizing some stuff already mentioned in the comments.) To add some context I will explicitly mention that the question originally suggested tag for cyclic sums.

Proposal: If a tag for this type of sums is created, it would be better to have both cyclic sums and symmetric sums under the same tag rather than a tag just for cyclic sums. (Perhaps the tag could be called something like or .)

Some relevant points:

  • These two types of sum are - to some extent - related.
  • I'd say that it's not unusual to have problems where both cyclic and symmetric sums occur. In such case, two tags might be relevant for the question. Having only five slots available for tags, taking up two slots by closely related tags might cause problems for having questions correctly tagged.

As far as I can tell, many questions about symmetric sums are now tagged using the tag. (If you check questions tagged or symmetric-polynomials+summation, symmetric-polynomials+inequality or symmetric-polynomials+contest-math you can find plenty of such questions. In some cases it's possible that this tag is not really suitable and the tag for cyclic sums would be a better fit.

Of course, symmetric sum is not always a symmetric polynomial, but typically it is closely related to some symmetric polynomials. (For example, cyclic sums appearing in some problems can be rewritten as a fraction in such a way that both numerator and denominator are symmetric polynomials.)

Close relation to the existing tag and existing usage suggest some potential problems:

  • Sometimes it might be unclear whether it's better to use the tag for symmetric polynomials or the tag for symmetric (and cyclic) sum. (I'd guess that a reasonable rule of thumb might be that the tag about symmetric sums is intended mostly for questions related to contest math.)
  • Since in the past the tag (symmetric-polynomials) was used in this context, probably a non-negligible number of questions might need retagging.

Despite the potential problems I think that having a single tag (cyclic-and-symmetric-sums) to use for some contest question might be better solution than to add to such question, for example, the three tags (cyclic-sums), (summation) and (symmetric-polynomials). (If they are applicable.)

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    $\begingroup$ I assume we could also include symmetric-functions in these considerations? Maybe this one could hold all the sums stuff. And the sym-poly could be reserved for questions about symmetric polynomials in a more narrow sense. Either way, I am skeptical that yet another 'symmetric' tag is needed, functions, polynomials, and now also sums, that seems a bit much to me. $\endgroup$
    – quid Mod
    May 10, 2019 at 14:23
  • $\begingroup$ I see your point. My main worry about separating the two is that there might be many questions where there will not be enough space to use all applicable tags. (Have you considered expanding the suggestion to keep (cyclic-sums) as a separate tag and symmetric-* tags separate as an answer? Usually not many people comment on tag-related threads - if there is an answer at least we would get some feedback through voting.) $\endgroup$
    – Martin Sleziak
    May 10, 2019 at 23:25
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    $\begingroup$ Except in a clear poll situation, I don't like posting answer in which I don't believe too much. My mind is not really made up, somehow I don't like the cyclic-sums tagn but I might be biased. $\endgroup$
    – quid Mod
    May 10, 2019 at 23:54

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