Optimal Penney Ante strategy via correlation polynomial identities.
Optimisation hybride par colonies de fourmis pour le problème de découpe à deux dimensions
Nous nous intéressons dans cet article au problème de découpe guillotine en deux dimensions noté 2BP/O/G. Il s'agit de découper un certain nombre de pièces rectangulaires dans un ensemble de plaques de matière première, elles même rectangulaires et identiques. Celles-ci sont disponibles en quantité illimitée. L'objectif est de minimiser le nombre de plaques utilisées pour satisfaire la demande, en appliquant une succession de coupes, dites guillotines, allant de bout en bout. Nous proposons une approche...
Optimization of an SMD placement machine and flows in parametric networks
In the minimization of the number of subtours made by the insertion head of an SMD placement machine a variant of the network flow problem arose. In a network with vertices and arcs a set of arcs (parametrized arcs) is given. The task is to find a flow of a given size such that the maximum of flow values along the arcs from is minimized. This problem can be solved by a sequence of maximum flow computations in modified networks where the capacities of the parametrized arcs are successively...
Optimum chemical balance weighing designs under the restriction on weighings
The paper deals with the problem of estimating individual weights of objects, using a chemical balance weighing design under the restriction on the number in which each object is weighed. A lower bound for the variance of each of the estimated weights from this chemical balance weighing design is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The incidence matrix of ternary balanced block design is used to construct optimum chemical balance weighing...
Orbit measures, random matrix theory and interlaced determinantal processes
A connection between representation of compact groups and some invariant ensembles of hermitian matrices is described. We focus on two types of invariant ensembles which extend the gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant probability measures on adjoint orbits of a compact Lie group. These measures are described by semiclassical approximation involving tensor and restriction multiplicities. We show that a large class of them are determinantal....
Order complex of ideals in a commutative ring with identity
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when...
Order of the smallest counterexample to Gallai's conjecture
In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Zamfirescu conjectured that the smallest counterexample to Gallai’s conjecture is a graph on 12 vertices. We prove that Gallai’s conjecture is true for every connected graph with , which implies that Zamfirescu’s conjecture is true.
Order Preserving or Increasing Mappings Freedom or Incomparability Preserving Mappings
Order statistics on colored permutations. (Statistiques d'ordre sur les permutations colorées.)
Order unicyclic graphs according to spectral radius of unoriented laplacian matrix
The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.
Ordered and linked chordal graphs
A graph G is called k-ordered if for every sequence of k distinct vertices there is a cycle traversing these vertices in the given order. In the present paper we consider two novel generalizations of this concept, k-vertex-edge-ordered and strongly k-vertex-edge-ordered. We prove the following results for a chordal graph G: (a) G is (2k-3)-connected if and only if it is k-vertex-edge-ordered (k ≥ 3). (b) G is (2k-1)-connected if and only if it is strongly k-vertex-edge-ordered...
Ordering Cacti With Vertices and Cycles by Their Laplacian Spectral Radii
Ordering the non-starlike trees with large reverse Wiener indices
The reverse Wiener index of a connected graph is defined as where is the number of vertices, is the diameter, and is the Wiener index (the sum of distances between all unordered pairs of vertices) of . We determine the -vertex non-starlike trees with the first four largest reverse Wiener indices for , and the -vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for .
Ordering the symmetric group: why using the Iwahori-Hecke algebra? (Ordonner le groupe symétrique: Pourquoi utiliser l'algèbre de Iwahori-Hecke?)
Ordering unicyclic graphs in terms of their smaller least eigenvalues.
Orders with ten elements are circle order.
Ordinal types in Ramsey theory and well-partial-ordering theory
Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency.
Ordres à distance minimum d'un tournoi et graphes partiels sans circuits maximaux
Ordres "C.A.C."