This volume includes thirty-three papers by eminent mathematicians, statisticians, and electrical engineers. The papers are organized into five main divisions: general problems of combinatorial mathematics; combinatorial problems of experimental designs; error-correcting codes and other problems of information theory; finite geometrics; and graphs. Many of the papers are followed by prepared discussions.
Contents
General Editor's Preface
Preface
Conference Participants
PART I. GENERAL PROBLEMS OF COMBINATORIAL MATHEMATICS
1. PROBABILISTIC METHODS IN COMBINATORIAL MATHEMATICS, by Alfred Renyi
2. COMBINATORIAL METHODS IN THE DISTRIBUTION OF kth POWER RESIDUES, by Alfred Brauer
3. ON CANONICAL BASES FOR SUBGROUPS OF AN ABELIAN GROUP, by Henry B. Mann
4. PERMANENTS AND SYSTEMS OF DISTINCT REPRESENTATIVES, by H. J. Ryser
5. ABEL IDENTITIES AND INVERSE RELATIONS, by John Riordan
6. ON THE AUTOMORPHISM GROUPS OF PALEY-HADAMARD MATRICES, by E. F. Assmus, Jr. and H. F. Mattson, Jr.
7. THE ELEMENTARY VECTORS OF A SUBSPACE OF RN, by R. T. Rockafellar
8. A COMBINATORIAL PROBLEM IN THE THEORY OF FREE MONO IDS, by A. Lentin and M. P. Schutzenberger
9. GENERALIZED MEASURE OF DISPERSION AND ANALYSIS OF DISTRIBUTIONAL PATTERN, by Tosio Kitagawa
PART II. COMBINATORIAL PROBLEMS OF EXPERIMENTAL DESIGNS
10. ON SYMMETRIC BLOCK DESIGNS WITH λ=2, by Marshall Hall, Jr.
11. ON SOME COMPOSITION AND EXTENSION METHODS IN THE CONSTRUCTION OF BLOCK DESIGNS FROM ASSOCIATION MATRICES, by I. M. Chakravarti and W. C. Blackwelder
12. ON THE NONEXISTENCE OF CERTAIN BLOCK DESIGNS, by Junjiro Ogawa
13. CALCULUS OF BLOCKS APPLIED TO PBIB DESIGNS, by Motosaburo Masuyama
14. ON THE APPLICATION OF HALF-NORMS TO CYCLIC DIFFERENCE SETS, by Koichi Yamamoto
15. ON EMBEDDING OF ORTHOGONAL ARRAYS OF STRENGTH TWO, by S. S. Shrikhande and Bhagwandas
PART III. ERROR-CORRECTING CODES AND OTHER PROBLEMS OF INFORMATION THEORY
16. FILE ORGANIZATION OF RECORDS WITH MULTIPLE-VALUED ATTRIBUTES FOR MULTI-ATTRIBUTE QUERIES, by R. C. Bose, C. T. Abraham and S. P. Ghosh
17. NEGACYCLIC CODES FOR THE LEE METRIC, by Elwyn R. Berlekamp
18. CODES AND IDEALS IN GROUP ALGEBRAS, by Mrs. Jessie MacWilliams
19. SOME NEW RESULTS ON FINITE FIELDS AND THEIR APPLICATION TO THE THEORY OF BCH CODES, by W. W. Peterson
20. WEIGHT DISTRIBUTIONS OF BOSE-CHAUDHURIHOCQUENGHEM CODES, by Tadao Kasami
21. IRREDUCIBLE POLYNOMIALS, SYNCHRONIZATION CODES, PRIMITIVE NECKLACES, AND THE CYCLOTOMIC ALGEBRA, by Solomon W. Golomb
22. A PROOF OF SOME PROPERTIES OF REED-MULLER CODES BY MEANS OF THE NORMAL BASIS THEOREM, by Paul Camion
23. EUCLIDEAN GEOMETRY CYCLIC CODES, by E. J. Weldon, Jr.
24. SOME CODES WHICH ARE INVARIANT UNDER A TRANSITIVE PERMUTATION GROUP AND THEIR CONNECTION WITH BALANCED INCOMPLETE BLOCK DESIGNS, by Shu Lin
PART IV. FINITE GEOMETRIES
25. CLASSIFICATION OF FINITE PROJECTIVE PLANES, by A. Barlotti
26. TRANSLATION PLANES OF ORDER p2, by T. G. Ostrom
27. CONSTRUCTION PROBLEMS OF FINITE PROJECTIVE PLANES, by R. H. Bruck
28. CYCLICAL GENERATION OF LINEAR SUBSPACES IN FINITE GEOMETRIES, by C. Radhakrishna Rao
PART V. GRAPHS
29. SOME CLASSES OF PERFECT GRAPHS, by C. Berge
30. A GEOMETRICAL VERSION OF THE FOUR COLOR PROBLEM, by W. T. Tutte
31. EDGE COLORINGS IN BIPARTITE GRAPHS, by Jon Folkman and D. R. Fulkerson
32. THE EIGENVALUES OF THE ADJACENCY MATRIX OF A GRAPH, by A. J. Hoffman
33. LABELLING TO OBTAIN A MAXIMUM MATCHING, by M. L. Balinski
Originally published in 1969.
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