A Survey of Combinatorial TheoryJagdish N. Srivastava 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
1 | |
15 | |
25 | |
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 |
453 | |
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Common terms and phrases
adjacency matrix Algebra array of strength association scheme asymptotic B-array balanced array balanced incomplete block bibd binary Canad clique code word columns combinatorial problem conjecture consider construction contains Corollary corresponding D. K. Ray-Chaudhuri defined denote digraphs distinct distribution edges elements Erdös error exactly exists finite fractional replicates GF(q given graph G Harary Hence hypergraph incidence matrix incomplete block designs independent intersect lattice Lemma line graph line-minimal linear lower bound majority decoding Math Mathematics methods North-Holland Publishing Company number theory obtained order statistics orthogonal arrays pair parameters parity check partial geometry partially balanced partition points polynômes polynomial positive integer prime Proc projective plane proof properties proved R. C. Bose random variables Rényi S. S. Shrikhande satisfies sequence sorting network space strongly regular graph subset symbols symmetric Theorem treatments upper bound values vertex vertices W. T. Tutte