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Previous peer review

This peer review discussion is closed.

I've listed this article for peer review because I am looking for (1) feedback on how to improve the article (2) an assessment of its rating.

For context: the last peer review was not completed because of a request for the articles on linear recurrences to be merged. That is now addressed and there are two articles left: this one, focusing on sequences, and linear recurrence with constant coefficients, (newly renamed), focusing on recurrences and how to solve them. The articles do not overlap substantially, but do link to each other.

All feedback welcome. Thanks, Caleb Stanford (talk) 04:12, 6 January 2022 (UTC)[reply]

Suggestions:

• The term "closed under" is used in the article without being wikilinked. Consider linking it in every section where it appears (the lead, In terms of vector spaces and Closure properties).
• The phrase "note that" is used in the article twice. Per MOS:NOTE, it should be removed.
• In Definition, the phrase "eventually-periodic sequences... which are disallowed by some authors" makes it sound like said authors explicitly disallow them, which is not the case (rather, they require that ${\displaystyle c_{d}\neq 0}$, which incidentally disallows such sequences). I think this sentence and the next one could use a rewrite.
• Every citation should have an exact page if possible, a page range should only be used if the claim(s) cited cannot be verified by reading any single page (and even then it should be as short as possible). I haven't checked whether the article complies with this, I just wanted to mention that. I see that the Reachability Problems source is used several times, you can provide a separate page number for each of them by using ((sfn)) or ((r)) but given that the page range isn't long it may be more trouble that it's worth.
• Speaking of which, the citations in Definition don't have a page number. I believe it should be page 66 in The Concrete Tetrahedron and page 1 in Skolem's Problem.
• The use of the notation ${\displaystyle s(n)}$ for an element of a sequence rather than the more common ${\displaystyle s_{n))$ can confuse readers, especially given that most (all?) articles linked from this one use the common notation. I propose changing ${\displaystyle s(n)}$ to ${\displaystyle s_{n))$ and ${\displaystyle F(n)}$ to ${\displaystyle F_{n))$.
• I've never seen the notation ${\displaystyle s(n)_{n\geq 0))$ before, it should be replaced by a more common notation such as ${\displaystyle (s(n))_{n=0}^{\infty ))$, or better yet, ${\displaystyle (s_{n})_{n=0}^{\infty ))$ (which mirrors the one used in the Sequence article). ${\displaystyle (s_{n})_{n\in \mathbb {N} ))$ is alright as long as you explain that ${\displaystyle \mathbb {N} }$ includes zero.
• It would be ideal if there were a source for every definition and every example, to verify that they are notable and therefore relevant to the article. Of particular interest would be a source for the fact that every eventually periodic sequence is constant-recursive, given that it causes a minor headache in Definition. That said, I don't think it's necessary.
• In the table in Closure properties, why is "Generating Function Equivalent" in title case?
• In Decision problems, "see closure properties" should be linked.

As for the rating, I think C-Class is accurate. It passes the C-Class standards, but not all of the B-Class criteria. I've never tried to do a B-Class review before, so take everything I say with a grain of salt.

1. The article is suitably referenced, with inline citations.

   I think this is the weak point of the article, and indeed of many Wikipedia articles about mathematical concepts. Not only are there important uncited statements in the article (although many of them can be verified by readers with sufficient mathematical background), as far as I can tell, all sources cited in the article are primary. The one thing that would improve the article most, in my opinion, is more secondary sources.

2. The article reasonably covers the topic, and does not contain obvious omissions or inaccuracies.

   This one needs review from a subject-matter expert.

3. The article has a defined structure.

   The article is well-organized, should pass this one.

4. The article is reasonably well-written.

   The prose is generally good, but it feels too textbook-like to me. Aside from the lead, the article uses a distinctive writing style that is more characteristic of a math textbook than of an encyclopedia.

5. The article contains supporting materials where appropriate.

   I think a video illustrating the concept would be helpful, but the article ought to pass this criterion even without one.

6. The article presents its content in an appropriately understandable way.

   I think the write one level down rule is the best way to assess this, but I don't know at which level this subject is typically studied. If graduate school, I'd say it passes. If undergraduate, it fails.

Please ping me in your replies. If you want me to ping you in my replies, please say so. Streded (talk) 11:57, 16 January 2022 (UTC)[reply]

@Caleb Stanford: Wasn't sure if you're watching this page, pinging you anyway. Streded (talk) 07:10, 18 January 2022 (UTC)[reply]

Dear @Streded: many thanks for the detailed and helpful review!

I'm working on these changes. I think your assessment is fair and I agree with the areas you identified for improvement. When I get the chance, I'll go through and improve the references and text throughout, and perhaps look at an A/FA-class math article for help with less textbook-sounding language. Yes, please ping me in replies (I do have this on my watchlist but easy to miss thing, sometimes my feed is a little messy.)

I think I'm going to copy your comments into a to-do list in the article talk page for checking off when they are done. Caleb Stanford (talk) 17:40, 18 January 2022 (UTC)[reply]

@Caleb Stanford: so far so good. A few extra comments:

• In Definition, the new phrasing of the second sentence feels cluttered. ${\displaystyle (s(n))_{n=0}^{\infty ))$ (${\displaystyle s(0),s(1),s(2),\dots }$) is difficult to parse because there are too many parentheses not separated by words. One way to write it that avoids this problem is "A sequence ${\displaystyle s(0),s(1),s(2),\dots }$ (written as ${\displaystyle (s(n))_{n=0}^{\infty ))$ using a shorthand notation), ranging...", but this is longer than the current sentence, so use your discretion.
• In In terms of vector spaces, the notation ${\displaystyle s(n+r)_{n\geq 0))$ is used instead of ${\displaystyle (s(n+r))_{n=0}^{\infty ))$. I'm also unsure about ${\displaystyle r\geq 0}$, but given that writing ${\displaystyle r\in \mathbb {N} }$ is ambiguous and the reader might not be familiar with ${\displaystyle \mathbb {N} _{0))$ it might be the best we can do.
• In In terms of generating functions, the sum is written as ${\displaystyle \sum _{n\geq 0}s(n)x^{n))$, this is legible but I think ${\displaystyle \sum _{n=0}^{\infty }s(n)x^{n))$ would be better.

Streded (talk) 22:12, 18 January 2022 (UTC)[reply]

@Streded: Thank you, fixed these as well. Caleb Stanford (talk) 22:34, 18 January 2022 (UTC)[reply]

@Caleb Stanford: You still have a couple of series in In terms of generating functions that use the other notation. I do like everything you've done in Definition so far :)

By the way, you have to sign in the same edit as pinging or else it doesn't work. I had to check my watchlist to see that you replied. See WP:PING for further info. Streded (talk) 13:19, 19 January 2022 (UTC)[reply]

@Caleb Stanford: Given that you already changed one sum, I assume you approve of this suggestion and just haven't had the time to implement it, so I went ahead and did it myself. Streded (talk) 04:35, 21 January 2022 (UTC)[reply]

@Streded:, yes that change is good. Thank you for proposing and making it! Eventually I will probably convert the sequence notation throughout to ${\displaystyle s_{n))$ instead of ${\displaystyle s(n)}$ as you also proposed. Caleb Stanford (talk) 16:04, 21 January 2022 (UTC)[reply]

@Caleb Stanford: I took the liberty of rewriting the first sentence in Polynomial sequences, please review and change or revert if you see fit. Streded (talk) 02:55, 30 January 2022 (UTC)[reply]