Combinatorial Representations
Definitions and brief description of applications (PowerPoint Presentation)
The presentation presents formal mathematical definition of graph representations. On the basis of this definition the main applications of the representations are also explained.
The approach within the framework of representations in AI (PowerPoint Presentation)
The issue of representation is recognized by AI community as a tool for solving problems. In this presentation it is demonstrated how combinatorial representations fit within this approach.
How the mathematical properties of graphs are reflected in engineering (PowerPoint Presentation).
A short presentation demonstrating the implication of self-duality of a graph upon the electronic circuit represented by it.
Examples of different engineering systems represented by graph representations (Flash).
Static beam system (represented by FGR, represented by FLGR); Dynamical system; Static frame; electrical circuit; mechanism;Stewart platform; Serial robot; Static pillar system; Highly coupled integrated system; Truss; Static cable system
The components of the combinatorial representation (Flash).
Each type of combinatorial representation is identified by its four main components: embedded knowledge, represented engineering domains, rules for construction and the relations to other combinatorial representations. Here you will find the exact definitions of all these representations.
The interactive map of combinatorial representations (Flash).
The map showing different types of combinatorial representations and different engineering fields represented by them. Click on different elements of the map to see more details.
For material on matroid representations we refer you to the paper of Dr. Offer Shai published in the Journal of Computing in Civil Engineering.