Last night I answered this question with a formula and a rationale. A little later someone else answered the same question using a different method with a formula that looks very different, which is fine. This morning, I found a direct combinatorial proof that the two formulas are equivalent. What should I do? What is proper MSE etiquette? Do I

  • add a comment to one of our posts (which one?) with the proof of equivalence, or

  • amend my answer with proof of equivalence, or

  • set up a community wiki, or

  • do nothing, or

  • do something else?

After considering the responses thru 11/12/17 noon I followed the second proposal on the list as suggested by @J. M. is not a mathematician. You can see the result by using the link above.

  • $\begingroup$ Why do you think either option is a good thing to do, or the only options which might be best to pursue? Unless the asker asks explicitly, "Why do I get two separate answers", (in which case, feel free to explain the equivalence in a comment) , I'd recommend you "do nothing." The only other option that I can suggest might be worth pursuing, is posting a Community Wiki post/answer, in which you credit each of your two answers as correct, and how they relate: where each implies the other. (Not just how your answer implies the other). $\endgroup$
    – amWhy
    Nov 11 '17 at 15:58
  • $\begingroup$ One answer can be equivalent (or lead to equivalent answers) with other answers. That happens all the time. The point you're leaving out is that how a question is answered (which approach), in one answer vs. another, can make all the difference to the asker, and/or the community. Which is most understandable to a student at the level at which the question is asked? etc. $\endgroup$
    – amWhy
    Nov 11 '17 at 16:08
  • 2
    $\begingroup$ I don't understand the close vote on this at all. $\endgroup$ Nov 11 '17 at 16:18
  • $\begingroup$ The current close vote suggests that the OP should flag for moderator attention. This is just wrong. @TrevorGunn . (But on the other hand, I am a bit annoyed by the OP making this discussion a voting type question) $\endgroup$
    – user99914
    Nov 11 '17 at 16:22
  • $\begingroup$ IMO, and I may be biased, my formula is a little messy but exhibits a natural approach to solving such problems, while the other one is neat and exhibits a great application of inclusion-exclusion. $\endgroup$ Nov 11 '17 at 16:50
  • $\begingroup$ @John Ma I was looking for alternatives. If I had had a few, should I have set up a poll? How? $\endgroup$ Nov 11 '17 at 16:55
  • $\begingroup$ Please do not set up a poll since (1) what you want is opinion, not numbers (2) One can act against the poll anyway in this situation, so why need a poll at all? (3) In general I prefer to vote only on big issues on the site. @StephenMeskin $\endgroup$
    – user99914
    Nov 11 '17 at 17:00
  • $\begingroup$ "I found a direct combinatorial proof that the two formulas are equivalent." - sounds like a good addendum to your answer, as long as you credit the other person. Why exactly were you reluctant to do this? $\endgroup$ Nov 11 '17 at 18:05
  • $\begingroup$ @J. M. is not a mathematician 1) I didn't figure out the equivalence at the same time as the answer. 2) The methods to get my answer and the equivalence are different and I don't want them to be entwined and confused with each other. $\endgroup$ Nov 11 '17 at 18:26
  • $\begingroup$ "I didn't figure out the equivalence at the same time as the answer." - that's perfectly fine; if you wish, delineate your previous paragraphs with a dividing horizontal line, and then put in the new content under it. People edit their posts all the time here. That should also hopefully address your second concern. $\endgroup$ Nov 11 '17 at 18:28
  • $\begingroup$ I would say that it depends on how complicated it is to prove that they are equivalent. If it's easy to see, you could just leave a short comment. $\endgroup$
    – Qudit
    Nov 12 '17 at 3:04
  • 2
    $\begingroup$ It can definitely be annoying though. I once answered a question using a simple argument based on expectation. Later, someone else answered it using essentially the same arguement but it was twice as long and was more complex due to using raw summations instead. The second answer was accepted and received twice as many upvotes as my earlier answer. $\endgroup$
    – Qudit
    Nov 12 '17 at 3:04

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