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