On posets of m-ary words

Computing Orbits of the Automorphism Group of the Subsequence Poset B m,n

“…Then we construct an isomorphism between D(n) and the subsequence poset B m,n , for n ≤ m. Conversely, suppose r = s and σ ∈ S r is a permutation such that β i = α σ (i) . To show that D(m) and D(n) are isomorphic we choose an element k = p δ1 1 p δ2 2 · · · p δr r of D(m) and define : (2) σ (2) · · · q δσ(r) σ (r) . Then is bijective and and −1 are order preserving functions, proving the lemma.…”

“…Following Burosch et al [2], we consider the top level word u m,n , in which u m,n is defined as the word a 1 , a 2 , ..., a n with a 1 = 0, a i+1 = a i + 1 (mod m) and a i ∈ . The subsequence poset where u m,n is the top level word is denoted by B m,n .…”

“…In this paper our notation is standard and taken mainly from [1,2] and [5,6]. For every positive integer n, D(n) and S n denote the set of all positive divisors of n and symmetric group on n symbols, respectively.…”

“…For every positive integer n, D(n) and S n denote the set of all positive divisors of n and symmetric group on n symbols, respectively. We encourage reader to consult [1][2][3] for discussion and background material about the subsequence poset B m,n .…”

A Finite Word Poset

“…In [5], Burosch, Gronau and Laborde studied the basic combinatorial properties of the poset B k,n for general k. They determined its Whitney numbers and they conjectured that this poset is Sperner and, even more, it is normal. In this paper we prove the analogous results for P (n) .…”