A Note on Free Regular Bands
Guoxin Liu · Journal of Southwest China Normal University · 2012
Let A be a non-empty set,and |A|=n.FA is a free semi-group on A.γ is the smallest free regular band congruence on FA.RA=FA/γ as a free regular band on the set FA and |RA| is the number of the element of RA.The paper proves that(u,v)∈γ if and only if i(u)=i(v),f(u)=f(v) and |RA|=sum((n k)~(k!)~2)from k=1 to n.