Computing orbits of the automorphism group of the subsequence poset \(B_{ m, n }\) (Q862978)

Let \(B_{m,n}\) be the set of all subwords obtained from a cyclic word of length \(n\) on an alphabet of \(m\) letters, provided with their natural order. In [Order 16, 179--194 (1999; Zbl 0958.06001)], \textit{G. Burosch, H.-D. Gronau} and \textit{J.-M. Lamborde} computed the automorphism group of the poset \(B_{m,n}\). The main goal of the present paper is to apply the above result in order to obtain all orbits of the natural action of \(\text{Aut}(B_{m,n})\) on \(B_{m,n}\). These orbits are precisely described in Theorem 3.