New bases for band varieties (Q1300545)

New bases of band varieties are constructed which are based on three families \(\{P_n\}\), \(\{Q_n\}\), \(\{R_n\}\) of words which are inductively defined by \(P_2=x_2\), \(Q_2=x_2x_1\), \(R_2=x_2x_1x_2\) and \(T_n=R_{n-1}x_n\overline T_{n-1}\) for \(T\in\{P,Q,R\}\) (and \(\overline T\) is the mirror image word of \(T\)). This refines the construction of bases of band varieties given earlier by \textit{J. A. Gerhard} and \textit{M. Petrich} [Proc. Lond. Math. Soc., III. Ser. 58, No. 2, 323-350 (1989; Zbl 0676.20038)].