In this paper we present a construction of every k-ary tree using a forest of (k− 1)ary trees satisfying a particular condition. We use this method recursively for the construction of the set of k-ary trees from the set of (k−1)-Dyck paths, thus obtaining a new bijection φ between these two sets. Furthermore, we introduce a new order on [k]∗ which is used for the full description of this biject...

It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y ) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y , there exists a hamiltonian path from u to v in the faulty k-ar...

By adopting natural generalizations of relational frame and relational model we showed in [2] that the deontic law D, Dp -» Op, is not universally first-order definable. In effect, we showed there that for n > 2, there is no n-adic first-order sentence p such that for every n-ary frame F,F ^D iff F ^(3 in the first-order sense. The notion of n-ary frame and model employed there may be summarize...

We determine the dimension of certain q-ary algebraic-geometric trace codes, extending previous results of Van Der Vlugt for p-ary algebraicgeometric trace codes.