[seqfan] Re: Seqfan Digest, Vol 36, Issue 1

[Ed Jeffery]

Seqfans,


Regarding A194923, what is the significance of writing "abelian square-free" rather than "square-free?"

Also, in the links for A194923Keränen writes: 


"It is easily seen that abelian squares cannot be avoided over a three letter alphabet. Indeed, in this alphabet, each word of length 8 contains an abelian square..."  

If the above assertion is true, since we are dealing with ternary abelian square-free words, doesn't it mean that the row of A194923 presumably containing words of length 8 should be written as {{}}, thus disrupting the integer sequence? On the other hand, aren't e.g. 01202120, 01020121and 01210201 square-free, or are they square-free but not abelian square-free? Please explain the difference.


Ed Jeffery