Talk:Necklace (combinatorics)

Justification for formula

There is no justification for any of the formulae given and it's not well documented anywhere else either. Would a derivation of each be a nice inclusion? RyanJM (talk) 14:30, 09 March 2011 (GMT)

Personally, I'd love to see a derivation too. In the mean time I put a reference tag to the Mathworld page. Though there's no derivation there either. Oh well, at least there's a reference now! WillieBlues (talk) 15:44, 5 April 2012 (UTC)

Merge from Bracelet (combinatorics)

This appears to be the same topic as discussed in Bracelet (combinatorics). Since this the name of this article is the more common term, I suggest that the other should be merged to here. Justin W Smith ^talk/_stalk 15:05, 14 May 2010 (UTC)

• No objection. Maxal (talk) 15:20, 14 May 2010 (UTC)

• Fine with me.—Emil J. 15:57, 14 May 2010 (UTC)

• They're not quite the same — one involves the action of the dihedral group (flipping as well as rotating) and the other is for the cyclic group (rotations only) — but they're so close that I think we should have only one article. So yes, please do merge them. —David Eppstein (talk) 16:00, 14 May 2010 (UTC)

Thanks for clarifying the distinction. Unless a reasonable objection comes up, I'll work on merging this weekend. It's a topic that I'm still learning about, so please verify the resulting merge. (I certainly won't be offended.) Justin W Smith ^talk/_stalk 16:30, 14 May 2010 (UTC)

• Agreed, but be sure to discuss the differences between the two. StuRat (talk) 17:01, 17 May 2010 (UTC)

• Merge complete. Justin W Smith ^talk/_stalk 23:27, 17 May 2010 (UTC)

Broken formula(s)

The current article contains this so-called "formula":

$\lim _{n\to \infty }\prod _{k=1}^{n}N_{k}(n)={\frac {k^{n}}{n!}}1(1+X)\left(1+X+X^{2}\right)\cdots \left(1+X+X^{2}+\cdots +X^{n-1}\right)$

Its incoherent-- the left hand side has n and k as bound variables, the right hand side contains both as free variables. 67.198.37.16 (talk) 19:35, 9 February 2018 (UTC)

Agreed. And this makes it confusing rather than informative. Also, the whole section § Products of necklaces is unsourced, so I'm going to be BOLD and delete it, pending its correction and a reliable source. yoyo (talk) 18:17, 14 April 2018 (UTC)

Done; section text hidden inside an HTML comment <!-- … --/> yoyo (talk) 18:24, 14 April 2018 (UTC)

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Definition

In the first paragraph, in the definition of a necklace, the explanation of an equivalence class ('a grouping for which there exists an equivalence relation') is rather bad. I think it should be either removed (would be my preferred solution, since 'equivalence class' is linked at any rate), or replaced by something correct ('a set of equivalent strings').

In the definition of a bracelet, it says 'a bracelet is a necklace such that...'. This is not correct and probably not meant. Couldn't it be changed to 'is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as well as the reverse as equivalent.'

GaloisGecko (talk) 16:04, 12 September 2020 (UTC)

I removed that rather poor definition of equivalence class. Perhaps someone will contribute a simpler definition of a necklace, but in the meantime I agree that's an improvement. Your other complaint also needs attention. Zaslav (talk) 16:28, 18 January 2022 (UTC)

Terminology

Is the term "fixed necklace" really used? It doesn't sound like a valid name for a cyclic equivalence class, as being fixed is just the opposite of rotation. I wonder if it is a neologism? Zaslav (talk) 16:25, 18 January 2022 (UTC)