We show that we can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.

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.

In this work, we propose a visual, custom-designed, event-driven interconnect simulation framework to evaluate the performance of off-chip multi-processor/memory communications architectures for line cards. The simulator uses the state-of-the-art software design techniques to provide the user with a flexible, robust and comprehensive tool that can evaluate k-ary n-cube based network topologies ...

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.