We study two topological properties of the 5-ary n-cube . Given two arbitrary distinct nodes x and y in , we prove that there exists an x-y path of every length ranging from 2n to 5n - 1, where n ≥ 2. Based on this result, we prove that is 5-edge-pancyclic by showing that every edge in lies on a cycle of every length ranging from 5 to 5n.
Markov Decision Processes (MDPs) are a classical framework for stochastic sequential decision problems, based on an enumerated state space representation. More compact and structured representations have been proposed: factorization techniques use state variables representations, while decomposition techniques are based on a partition of the state space into sub-regions and take advantage of the resulting structure of the state transition graph. We use a family of probabilistic exploration-like...
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Motivated by the wavelength division multiplexing in all-optical networks, we consider the problem of finding an optimal (with respect to the least possible number of wavelengths) set of internally node disjoint dipaths connecting all pairs of distinct nodes in the binary -dimensional hypercube, where . This system of dipaths constitutes a routing protocol that remains functional in the presence of up to faults (of nodes and/or links). The problem of constructing such protocols for general...
We show that the pairs where T is a tree and its dual are the only maximal antichains of size 2 in the category of directed graphs endowed with its natural homomorphism ordering.
For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.
For any finite word w on a finite alphabet, we consider the basic parameters Rw and Kw of w defined as follows: Rw is the minimal natural number for which w has no right special factor of length Rw and Kw is the minimal natural number for which w has no repeated suffix of length Kw. In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.