Talk:Lyndon word

message: This was requested! however all it really entails is a definition...perhaps a redirect? Wikipedia appears to be lacking in general on the broader subject however. Robbjedi 04:45, 18 October 2005 (UTC)
thread_title: New article created

message: I am not merging this into necklace (combinatorics), as Lyndon word is a standalone concept, deserving its own article. Hope nobody minds. Kompas 09:49, 3 August 2006 (UTC)
thread_title:  Necklace 

message: needs a reference 173.206.238.69 (talk) 00:26, 21 May 2012 (UTC)
replies: text: Done. -- Darij (talk) 09:36, 24 December 2015 (UTC)
thread_title:  "A theorem of Radford states...." 

message: What's wrong to include the strings "00", "11" etc. in the sequence? --RokerHRO (talk) 15:17, 7 July 2014 (UTC)
replies: text: They are equal to their rotations, and therefore are not the unique smallest string among their rotations. Also because then the standard factorization wouldn't work. —David Eppstein (talk) 16:02, 7 July 2014 (UTC)
thread_title:  Why periodic strings are omitted? 

message: (For starters, English is not my primary language..)
My first understanding of this was:
Every binary Lyndon word of each length has its own number.
Probably just my fault, but wouldnt the word amounts be a tiny bit more exact? Although it doesnt sound that good. Or could someone think of another way to say it?
Anyway, if anyone else had trouble understanding, the sequence 1, 2, 1, ... means:
* 1 word of length 0 - ε
* 2 words of length 1 - 0,1
* 1 word of length 2 - 01
* ...  — Preceding unsigned comment added by 147.32.31.193 (talk) 18:18, 5 November 2014 (UTC)
thread_title:  The numbers of binary Lyndon words of each length 

message: I have tweaked the definition to regard the empty word as non-Lyndon. There are multiple reasons for this:
* Several references used on this page (e.g., Lothaire, Kufleitner, Brlek-Lachaud-Provencal-Reutenauer) define a Lyndon word to be nonempty. Some others (e.g., Berstel-Pocchiola, Ruskey and Melancon) make claims incompatible with the empty word being Lyndon (e.g., Melancon about the basis of the free Lie algebra, and Berstel-Pocchiola when they list all Lyndon words of length up to 5).
* The claim that "every string may be formed in a unique way by concatenating a sequence of Lyndon words, in such a way that the words in the sequence are nonincreasing lexicographically" would be false if the empty word were Lyndon, since the possibility of adding or removing the empty word at the end of the sequence would break the uniqueness.
* Duval's algorithm does not work when started with the empty word.
* In Radford's theorem, the empty word is out of place too. -- Darij (talk) 09:36, 24 December 2015 (UTC)
thread_title:  Nonemptiness 

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thread_title:  External links modified