A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertexdisjoint subtrees of T whose orders are given by τ ; from a result by Barth and Fournier it follows that ∆(T ) ≤ 4. A necessary and a sufficient condition for being an arbitrarily vertex decomposable star-like tree have been exhibited. The conditions se...

In this paper we show that the sets of plusrespectively minus-decomposable permutations of a regular class under the rank encoding form regular sublanguages. Plusrespectively minus-decomposable permutations are permutations allowing for a special kind of block-decomposition. The language theoretic results shown have di erent approaches, even though the properties of plusand minus-decomposabilit...

Symmetrizations of tensors by irreducible characters of the symmetric group serve as natural analogues of symmetric and skew-symmetric tensors. The question of when a symmetrized decomposable tensor is non-zero is intimately related to the rank partition of a matroid extracted from the tensor. In this paper we characterize the non-vanishing of the symmetrization of certain partially symmetrized...

The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to oating-point arithmetic. The resulting ADZ method enables one to generate decomposable data structures | both labelled or unlabelled | uniformly at random, in expected O(n ) time and space, after a preprocessing phase of O(n ) time, which reduces to O(n ) f...

It is well-known that all orthogonal arrays of the form OA(N, t+1, 2, t) are decomposable into λ orthogonal arrays of strength t and index 1. While the same is not generally true when s = 3, we will show that all simple orthogonal arrays of the form OA(N, t + 1, 3, t) are also decomposable into orthogonal arrays of strength t and index 1.