On posets of m-ary words Original Research Article

The posetBm, n, which consists of the naturally ordered subwords of the cyclic word on length n on an alphabet of m letters, where subwords are obtained by deleting letters, is introduced and studied. This poset is of special interest since it is strongly related to several different structured posets, like Boolean lattices, chains, Higman orders and Kruskal-Katona posets.