A Survey of Combinatorial Theory

Front Cover
Jagdish N. Srivastava
Elsevier, May 12, 2014 - Biography & Autobiography - 476 pages
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.
 

Contents

CHAPTER 1 Some Classical and Modern Topics in Finite Geometrical Structures
1
CHAPTER 2 Balanced Hypergraphs and Some Applications to Graph Theory
15
CHAPTER 3 A Strongly Regular Graph Derived from the Perfect Ternary Golay Code
25
CHAPTER 4 Characterization Problems of Combinatorial Graph Theory
31
CHAPTER 5 Lineminimal Graphs with Cyclic Group
53
CHAPTER 6 Circle Geometry in Higher Dimensions
69
CHAPTER 7 Bose as TeacherThe Early Years
79
CHAPTER 8 Construction of Symmetric Hadamard Matrices
81
CHAPTER 21 A Survey of Graphical Enumeration Problems
259
CHAPTER 22 On Spectrally Bounded Graphs
277
CHAPTER 23 Combinatorial Search Problems
285
CHAPTER 24 Some Problems in Combinatorial Geometry
309
CHAPTER 25 Recent Developments in India in the Construction of Confounded Asymmetrical Factorial Designs
313
CHAPTER 26 Combinatorial Problems in Communication Networks
323
CHAPTER 27 On Hadamard Difference Sets
333
CHAPTER 28 On the Randomization of Block Designs
335

CHAPTER 9 Cayley Diagrams and Regular Complex Polygons
85
CHAPTER 10 Combinatorial Problems in Finite Abelian Groups
95
CHAPTER 11 A qAnalog of the Partition Lattice
101
CHAPTER 12 Problems and Results on Combinatorial Number Theory
117
CHAPTER 13 Dissection Graphs of Planar Point Sets
139
CHAPTER 14 Some Combinatorial Problems and Results in Fractional Replication
151
CHAPTER 15 The BoseNelson Sorting Problem
163
CHAPTER 16 Nombres dEuler et Permutations Alternantes
173
CHAPTER 17 Some Combinatorial Aspects of Coding Theory
189
CHAPTER 18 Some Augmentations of BoseChaudhuri Error Correcting Codes
209
CHAPTER 19 On Order Statistics and Some Applications of Combinatorial Methods in Statistics
217
CHAPTER 20 Construction of Block Designst
251
CHAPTER 29 Some Combinatorial Problems of Arrays and Applications to Design of Experimentst
349
CHAPTER 30 The Existence of Resolvable Block Designs
361
CHAPTER 31 Variants of v k λDesigns
377
A Systems Concept
385
CHAPTER 33 On the Problem of Construction and Uniqueness of Saturated Designs
397
CHAPTER 34 Strongly Regular Graphs and Symmetric 3Designs
403
CHAPTER 35 Balanced Arrays and Orthogonal Arrays
411
CHAPTER 36 On Software Validation
429
CHAPTER 37 The Enumerative Theory of Planar Maps
437
CHAPTER 38 A Construction for Room Squares
449
Author Index
453
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