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::I find it interesting that my way puts the dots at a level where the omitted text would have been and your way puts the dots at a level where the immediately adjacent (not-omitted) text is. For example, I would write a set of binary operators as {{tmath|\{{mset|+, -, \times, \cdots\}}}} rather than {{tmath|\{{mset|+, -, \times, \ldots\}}}}.
::I agree that generally it would be awkward to omit the addition sign immediately before the ellipsis of a series. If we're looking for a contrived exception... suppose for each term you get to flip a coin to decide whether the next term is positive or negative. The the series might end up looking like {{tmath|{}-1 - x + x^2 + x^3 - x^4 + x^5 - x^6 \cdots}}. Yes, I warned you it was contrived. Would you also use cdots there? —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]] ([[User talk:Quantling|talk]] | [[Special:Contributions/Quantling|contribs]]) 18:42, 15 July 2025 (UTC)
:::In your contrived example the correct thing to do is either <math>-x^6 \pm \cdots</math> or <math>-x^6 \pm \ldots</math>. Personally I tend to use ldots when the operation is addition, but \cdots looks a lot better following \pm for some reason. --[[User:JayBeeEll|JBL]] ([[User_talk:JayBeeEll|talk]]) 00:47, 16 July 2025 (UTC)
:::In your example, you should not omit the operation. As JBL says, use {{tmath|\pm}}. In your other example, I'd go for the lower dots when using commas, even if the entries are centered. I have never seen this come up though. Anyway, if you want to consistently use 'ldots' on some page or other, that's probably fine; there are some authors who do that, and according to Wikipedia (with questionable sourcing) it's standard in Russian mathematical typesetting. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 04:06, 16 July 2025 (UTC)
::::It case it isn't clear ... I wouldn't ever escalate this to an edit war or any formal dispute, because I know that my approach is only one of several. I continue this discussion only because I find the topic interesting that there are these multiple ways. And maybe I can learn something.
::::Because I'm contriving the example, I could make it a three-sided coin where the next term is either added, subtracted, or omitted. Or it could be addition vs. subtraction vs. a binary operation {{math|*}} signifying some other binary operation under discussion. Maybe then we'd put the ellipsis (centered or lowered) starting after a term rather than after a binary operator. Or maybe you have syntax that generalizes {{tmath|\pm}} that would handle that too!
::::But even with just addition and subtraction... conceptually the random choices being made are to extend the sequence with {{tmath|{}-x^4}}, then {{tmath|{}+x^5}}, then {{tmath|{}-x^6}}, etc. so it seems wrong to me to place the ellipsis into the middle of one of those extending steps.
::::But that's all contrived stuff. ''The part that actually interests me'': If we expand to include areas outside of mathematics, is there a general rule for how high to put the ellipses? In this more general context I wonder how my preference to put the ellipses at the level roughly where the start of the omitted text would be balances with the preference to put the ellipsis at the level where the last of the previous not-omitted text is. Perhaps the answer is boring (at least for English): is it that only in mathematics do we ever use anything other than ldots? —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]] ([[User talk:Quantling|talk]] | [[Special:Contributions/Quantling|contribs]]) 14:14, 16 July 2025 (UTC)
:::::FWIW, ChatGPT disagrees with me: {{!tq|Does the level that the ellipsis is placed depend upon the omitted text's level or the level of the surrounding text?}} {{tq|... the placement of an ellipsis depends primarily on the level and type of the surrounding text—not on the content that is being omitted.}} —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]] ([[User talk:Quantling|talk]] | [[Special:Contributions/Quantling|contribs]]) 15:22, 16 July 2025 (UTC)
::::::Please don't try to use ChatGPT to answer research questions. It is literally a stochastic bullshit generator. (Feel free to use ChatGPT to write bad poetry, compose corporate emails, or whatever.) –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 18:48, 16 July 2025 (UTC)
:::::If your example is so complicated that readers can't obviously figure it out, please just explain with prose instead of letting them infer from tiny subtle differences of notation. As for non-mathematical typography: an ellipsis is ordinarily used for omitting words or sentences in the middle of running prose. In that context it doesn't really make too much sense to change their alignment. I imagine in other kinds of more structured two-dimensional notation other orientations or alignments of ellipses could be used (chemical equations?) but I don't know of any off hand. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 18:49, 16 July 2025 (UTC)
::::::{{tq|Please don't try to use ChatGPT to answer research questions.}} — I agree with you, despite that ChatGPT's answer to your statement suggests nuances and exceptions.
::::::{{tq|... explain with prose instead of letting them infer from tiny subtle differences of notation}} — generally I aim to do both. —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]] ([[User talk:Quantling|talk]] | [[Special:Contributions/Quantling|contribs]]) 19:20, 16 July 2025 (UTC)
== Is there a generating function ==
I noticed in the part where it said generating function it did not go in to terms on how to make Fn without writing the whole list, just in something else. Also , the connection to Pascal’s triangle is important and should be added [[Special:Contributions/2A00:23C7:9910:EE01:295C:A9B5:540B:86B|2A00:23C7:9910:EE01:295C:A9B5:540B:86B]] ([[User talk:2A00:23C7:9910:EE01:295C:A9B5:540B:86B|talk]]) 09:39, 18 July 2025 (UTC)
:I don't understand your question about the generating function. As for your other point, the article has a diagram and the line 'The Fibonacci numbers occur as the sums of binomial coefficients in the "shallow" diagonals of Pascal's triangle'. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 10:03, 18 July 2025 (UTC)
:I have added the standard way for computing the generating series. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 10:32, 18 July 2025 (UTC)
::I edited the article before seeing this discussion. I apologize for that. Hopefully, the edit I made will be considered constructive nonetheless. If not, please revert or otherwise do the right thing. Thank you —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]] ([[User talk:Quantling|talk]] | [[Special:Contributions/Quantling|contribs]]) 13:16, 18 July 2025 (UTC)
:::I removed the section since its understandable part contains only assertions that are elsewhere in the article. Flajolet et al. systematic use of generating series (even when they are never convergent) is interesting and very powerful, but I do not se any reason for mentioning it in this article. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 21:13, 18 July 2025 (UTC)
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