tag:blogger.com,1999:blog-20067416.post3032964576456885846..comments2022-11-23T07:53:11.449-05:00Comments on Recursivity: Combinatorics on Words, A Puzzle, and a Silly Research ProposalUnknownnoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-20067416.post-44487790039264741322007-08-14T16:51:00.000-04:002007-08-14T16:51:00.000-04:00David:"Horseshoer" is a nice one! Thanks.David:<BR/><BR/>"Horseshoer" is a nice one! Thanks.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-10949860820013115372007-08-14T15:35:00.000-04:002007-08-14T15:35:00.000-04:00my wordlist also has an engish abelian square "hor...my wordlist also has an engish abelian square "horseshoer".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-20067416.post-71894693611388685502007-08-13T18:19:00.000-04:002007-08-13T18:19:00.000-04:00There are indeed some connections with group theor...There are indeed some connections with group theory. Note that the set of all words over a finite alphabet form a free monoid (or, if you don't count the empty word, a semigroup), not a group. Of course, you can always add inverses, if you like, to get a free group.<BR/><BR/>I don't know any purely group-theoretic approach to Thue's result on three letters. However, people have applied Thue's result and related ones to problems in group theory, such as Burnside's problem. <BR/><BR/>As for avoiding abelian squares, that does have some group-theoretic aspects. There is a famous paper by Dekking that uses a group-theoretic approach to construct words avoiding higher abelian powers.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-55557318946149493982007-08-13T17:47:00.000-04:002007-08-13T17:47:00.000-04:00Hmmm, it seems as if the "square free" problem wou...Hmmm, it seems as if the "square free" problem would have a group theoretic solution.Harriethttps://www.blogger.com/profile/17953435368705942387noreply@blogger.com