For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. We discuss the properties of the construction and two simple examples. 1991 Mathematics Subject Classification: 17A42, 16Y99, 17A40

We study the space requirement of m-ary search trees under the random permutation model when m ≥ 27 is fixed. Chauvin and Pouyanne have shown recently that Xn, the space requirement of an m-ary search tree on n keys, equals μ(n + 1) + 2Re [Λn2 ] + nn Reλ2 , where μ and λ2 are certain constants, Λ is a complex-valued random variable, and n → 0 a.s. and in L as n → ∞. Using the contraction method...

We consider algebras with a single n-ary operation and a certain type of associativity.We prove that up to isomorphism there are exactly 5 of these associative mono-n-ary algebras with 2 elements for even n ≥ 2 and 6 for odd n ≥ 3. These algebras are described explicitly. It is shown that a similar result is impossible for algebras with at least 4 elements. An application concerning the assignm...

Lee distance Gray codes for k-ary n-cubes and torus networks are presented. Using these Lee distance Gray codes, it is further shown how to directly generate edge disjoint Hamiltonian cycles for a class of k-ary n-cubes, 2-D tori, and hypercubes.

The k-ary n-cube is one of the most popular interconnection networks for parallel and distributed systems. Strong matching preclusion that additionally permits more destructive vertex faults in a graph is amore extensive formof the originalmatching preclusion that assumes only edge faults. In this paper, we establish the strong matching preclusion number and all minimum strong matching preclusi...

Given an n-ary k-valued function f , gap(f) denotes the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f . We particularly solve a problem concerning the explicit determination of n-ary k-valued functions f with 2 ≤ gap(f) ≤ n ≤ k. Our methods yield new combinatorial results about the number of such functions.

In this paper we have developed an algorithm that converts a given k-ary tree, for any k ≥ 3, to its equivalent binary tree structure. The binary tree is generated in O(n) time, for a k-ary tree with a total of n nodes. The algorithm is designed aiming at reducing the height of the constructed binary tree. The constructed tree does not contain any free links in the non-leaf nodes. That means th...

This paper proposes a model of adding relations between members of the same level in a pyramid organization structure which is a complete K-ary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between one node and every other node with the same depth N in a complete K-ary tree of height H are added, an optimal depth ...

In this paper, for an odd prime p, two positive integers n, m with n = 2m, and pm ≡ 1 (mod 4), we derive an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a p-ary m-sequence. The two decimation factors are 2 and 2(pm + 1), and the upper bound is derived as 3 2 p m + 2 . In fact, those two sequences correspond to the p-ary sequences used for the...