A Survey of Combinatorial Theory

A Survey of Combinatorial Theory covers the papers presented at the International Symposium on Combinatorial Mathematics and its Applications, held at Colorado State University (CSU), Fort Collins, Colorado on September 9-11, 1971. The book focuses on the principles, operations, and approaches involved in combinatorial theory, including the Bose-Nelson sorting problem, Golay code, and Galois geometries.

The selection first ponders on classical and modern topics in finite geometrical structures; balanced hypergraphs and applications to graph theory; and strongly regular graph derived from the perfect ternary Golay code. Discussions focus on perfect ternary Golay code, finite projective and affine planes, Galois geometries, and other geometric structures. The book then examines the characterization problems of combinatorial graph theory, line-minimal graphs with cyclic group, circle geometry in higher dimensions, and Cayley diagrams and regular complex polygons.

The text discusses combinatorial problems in finite Abelian groups, dissection graphs of planar point sets, combinatorial problems and results in fractional replication, Bose-Nelson sorting problem, and some combinatorial aspects of coding theory. The text also reviews the enumerative theory of planar maps, balanced arrays and orthogonal arrays, existence of resolvable block designs, and combinatorial problems in communication networks.

The selection is a valuable source of information for mathematicians and researchers interested in the combinatorial theory.

Contenu

Preface

1. Some Classical and Modern Topics in Finite Geometrical Structures

2. Balanced Hypergraphs and Some Applications to Graph Theory

3. A Strongly Regular Graph Derived from the Perfect Ternary Golay Code

4. Characterization Problems of Combinatorial Graph Theory

5. Line-Minimal Graphs with Cyclic Group

6. Circle Geometry in Higher Dimensions

7. Bose as Teacher-The Early Years

8. Construction of Symmetric Hadamard Matrices

9. Cayley Diagrams and Regular Complex Polygons

10. Combinatorial Problems in Finite Abelian Groups

11. A q-Analog of the Partition Lattice

12. Problems and Results on Combinatorial Number Theory

13. Dissection Graphs of Planar Point Sets

14. Some Combinatorial Problems and Results in Fractional Replication

15. The Bose-Nelson Sorting Problem

16. Nombres d'Euler et Permutations Alternantes

17. Some Combinatorial Aspects of Coding Theory

18. Some Augmentations of Bose-Chaudhuri Error Correcting Codes

19. On Order Statistics and Some Applications of Combinatorial Methods in Statistics

20. Construction of Block Designs

21. A Survey of Graphical Enumeration Problems

22. On Spectrally Bounded Graphs

23. Combinatorial Search Problems

24. Some Problems in Combinatorial Geometry

25. Recent Developments in India in the Construction of Confounded Asymmetrical Factorial Designs

26. Combinatorial Problems in Communication Networks

27. On Hadamard Difference Sets

28. On the Randomization of Block Designs

29. Some Combinatorial Problems of Arrays and Applications to Design of Experiments

30. The Existence of Resolvable Block Designs

31. Variants of (v, k, )-Designs

32. Coding Need: A System's Concept

33. On the Problem of Construction and Uniqueness of Saturated 2KR-p Designs

34. Strongly Regular Graphs and Symmetric 3-Designs

35. Balanced Arrays and Orthogonal Arrays

36. On Software Validation

37. The Enumerative Theory of Planar Maps

38. A Construction for Room Squares