Periodic balanced binary triangles

The Ill-Balanced Triangles of the Islamic States in Crisis

The 4-error linear complexity distribution for $2^n$-periodic binary sequences

By using the sieve method of combinatorics, we study k-error linear complexity distribution of 2-periodic binary sequences based on Games-Chan algorithm. For k = 4, 5, the complete counting functions on the k-error linear complexity of 2-periodic balanced binary sequences (with linear complexity less than 2) are presented. As a consequence of the result, the complete counting functions on the 4...

A particle swarm optimization method for periodic vehicle routing problem with pickup and delivery in transportation

In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods...

A universal sequence of integers generating balanced Steinhaus figures modulo an odd number

In this paper, we partially solve an open problem, due to J. C. Molluzzo in 1976, on the existence of balanced Steinhaus triangles modulo a positive integer n, that are Steinhaus triangles containing all the elements of Z/nZ with the same multiplicity. For every odd number n, we build an orbit in Z/nZ, by the linear cellular automaton generating the Pascal triangle modulo n, which contains infi...

Dynamic Ray Shooting and Shortest Paths in Planar Subdivisions via Balanced Geodesic Triangulations

We give new methods for maintaining a data structure that supports ray-shooting and shortest-path queries in a dynamically changing connected planar subdivision S . Our approach is based on a new dynamic method for maintaining a balanced decomposition of a simple polygon via geodesic triangles. We maintain such triangulations by viewing their dual trees as balanced trees. We show that rotations...