Talk:Constant-recursive sequence: Difference between revisions

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== Be more explicit about eventually-periodic case ==

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: [[User:Eric Rowland|Eric Rowland]], does this address your objections? [[User:Streded|Streded]] ([[User talk:Streded|talk]]) 04:10, 27 January 2022 (UTC)

== To -do list for [[Wikipedia:Good article criteria]] (June 2022) ==

Trying to bring this to GA status eventually. [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 22:32, 22 June 2022 (UTC)

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::*Concrete Tetrahedron is a solid reference, but covers only about half of the material in the article (mostly the more elementary stuff). Also, because it doesn't allow eventually-periodic we should avoid relying on it too heavily for citing results.

::*I took a look at Concrete Mathematics but it doesn't cover most of the material in the article (in fact we could probably remove it from Further Reading).

::{{done}}

:*Probably some combinatorics and generating functions textbooks will cover the relevant material, that's where I will look first.

::{{done}} (added ref to Stanley)

:*We need references for every line in the Closure Properties table.

::{{done}} (added refs to Stanley)

:*Finally, a few statements in the lead still need references.

::{{not done}} per [[MOS:LEADCITE]]

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{{Talk:Constant-recursive sequence/GA1}}

== Degeneracy ==

{{ping|GaseousButter}} I corrected your edit as I think you meant "if k = 1" not "if n = 1", but let me know if I got the result wrong! [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 23:41, 1 July 2024 (UTC)

:Thank you - I was transcribing directly from the book but then changed the letters to match with the article - that n slipped through the cracks it seems! [[User:GaseousButter|GaseousButter]] ([[User talk:GaseousButter|talk]]) 13:37, 4 July 2024 (UTC)

== Skolem problem ==

"For example, the Skolem problem is decidable for sequences of order up to 4"

It would do to be more precise here - what is currently published in the literature is that the Skolem problem is decidable for algebraic sequences of order up to 3, and '''real''' algebraic sequences up to order 4. In fact, it is true that it is decidable for all algebraic sequences up to order 4 - I have a paper in the works about that so watch this space ;). But as of now what is written is a little ambiguous and potentially misleading. [[User:GaseousButter|GaseousButter]] ([[User talk:GaseousButter|talk]]) 13:48, 4 July 2024 (UTC)

:Thanks, I can fix this! From the source (Ouaknine and Worrell) I have: "Partial progress towards decidability of the Skolem Problem has been achieved by restricting the order of linear recurrence sequences. For sequences of order 1 and 2, decidability is relatively straightforward and considered to be folklore. Decidability for orders 3 and 4, however, had to wait until the 1980s before being independently settled positively by Mignotte, Shorey, and Tijdeman [13], as well as Vereshchagin"

:so I guess they are referring to real algebraic sequences? I can also check the original sources and add these. Or feel free to propose an edit. Thanks! [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 19:05, 6 July 2024 (UTC)

::Yes, in that source you cited the way they define a linear recurrence sequence is to be over the reals. I think the best thing to do is to cite the original sources (they're not the nicest things to read through being from the 80s). I might edit it myself in a bit but I was originally being lazy because I didn't want to figure out what the cleanest wording would be haha [[User:GaseousButter|GaseousButter]] ([[User talk:GaseousButter|talk]]) 19:02, 16 July 2024 (UTC)