[seqfan] Re: A certain semigroup

[David Newman]

I see your problem and perhaps I could have done better in posing the
question.  I agree that what I have described is not an equivalence
relation.

The triple {S1,S2,S3} or

 {{a,b,b,a,c,c,b},{b,a,a,b,c,c,b},{b,a,a,c,b,b,c}}
which you've mentioned, counts as one element of the set which I am trying
to count.  No other words belong in there because no others are equivalent
to either S1, S2, or S3.

Does this answer your question?  Or am I leaving myself open to several
interpretations?