Combinatorial 3-D Sequencing Theory and Methods in Applied Mechanics
by
Vladimir V. Riznyk
Lviv Polytechnic State University, Dept.of Computer Aided Control Systems, 12 Bandera Street, 290646 Lviv, Ukraina

Combinatorial 3-D Sequencing Theory, namely the concept of Three-dimensional Ideal Ring Bundles (3D-IRBs), can be used for finding optimal solutions for wide classes of problems in applied mechanics. 3D-IRBs are cyclic sequences of integer 3D-vectors which form perfect 3D-partitions of a finite 3D-space of vectors. The vector sums of connected sub-sequences of 3D-IRB enumerate the set of integer 3D-vectors exactly k-times. This property makes 3D-IRBs useful in applications which need to partition sets with the smallest possible number of intersections. Applications profiting from Combinatorial 3-D Sequencing Theory are for example synthesis of nonredundant aperture mask systems for holohraphic image, 3D-image coding and compression, pattern recognition and three-dimensional image analysis.

Date received: February 17, 1999