Optimum Vector Combinatorial Theory and Its Applications

Authors: Riznyk V*

DOI: 10.23880/art-16000122

Volume 3, Issue 1

Abstract

Optimum vector combinatorial theory, namely the concept of Ideal Ring Bundles (IRBs), can be used for finding optimal solutions for wide classes of scientific and technological problems. IRBs are cyclic sequences of positive integers which form perfect partitions of a finite interval [1, s] of integers. The sums of connected sub-sequences of a numerical IRB enumerate the set of integers [1, s-1] exactly k-times. Example: The numerical IRB {1,3,2,7} containing four elements allows an enumeration of all numbers 1=1, 2=2, 3=3, 4=1+3, 5=3+2, 6=1+3+2, …12= 3+2+7 exactly once.

Keywords: Ideal Ring Bundle; Rotational Symmetry; PDP; Torus Coordinate System; Combinatorial Optimization; Optimum Vector Monolithic Code

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