Combinatorial Mathematics and Its Applications

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.ContentsGeneral Editor’s PrefacePrefaceConference ParticipantsPART I. GENERAL PROBLEMS OF COMBINATORIAL MATHEMATICS1. PROBABILISTIC METHODS IN COMBINATORIAL MATHEMATICS, by Alfred Renyi2. COMBINATORIAL METHODS IN THE DISTRIBUTION OF kth POWER RESIDUES, by Alfred Brauer3. ON CANONICAL BASES FOR SUBGROUPS OF AN ABELIAN GROUP, by Henry B. Mann4. PERMANENTS AND SYSTEMS OF DISTINCT REPRESENTATIVES, by H. J. Ryser5. ABEL IDENTITIES AND INVERSE RELATIONS, by John Riordan6. 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. Rockafellar8. A COMBINATORIAL PROBLEM IN THE THEORY OF FREE MONO IDS, by A. Lentin and M. P. Schutzenberger9. GENERALIZED MEASURE OF DISPERSION AND ANALYSIS OF DISTRIBUTIONAL PATTERN, by Tosio KitagawaPART II. COMBINATORIAL PROBLEMS OF EXPERIMENTAL DESIGNS10. 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. Blackwelder12. ON THE NONEXISTENCE OF CERTAIN BLOCK DESIGNS, by Junjiro Ogawa13. CALCULUS OF BLOCKS APPLIED TO PBIB DESIGNS, by Motosaburo Masuyama14. ON THE APPLICATION OF HALF-NORMS TO CYCLIC DIFFERENCE SETS, by Koichi Yamamoto15. ON EMBEDDING OF ORTHOGONAL ARRAYS OF STRENGTH TWO, by S. S. Shrikhande and BhagwandasPART III. ERROR-CORRECTING CODES AND OTHER PROBLEMS OF INFORMATION THEORY16. FILE ORGANIZATION OF RECORDS WITH MULTIPLE·VALUED ATTRIBUTES FOR MULTI-ATTRIBUTE QUERIES, by R. C. Bose, C. T. Abraham and S. P. Ghosh17. NEGACYCLIC CODES FOR THE LEE METRIC, by Elwyn R. Berlekamp18. CODES AND IDEALS IN GROUP ALGEBRAS, by Mrs. Jessie MacWilliams19. SOME NEW RESULTS ON FINITE FIELDS AND THEIR APPLICATION TO THE THEORY OF BCH CODES, by W. W. Peterson20. WEIGHT DISTRIBUTIONS OF BOSE-CHAUDHURIHOCQUENGHEM CODES, by Tadao Kasami21. IRREDUCIBLE POLYNOMIALS, SYNCHRONIZATION CODES, PRIMITIVE NECKLACES, AND THE CYCLOTOMIC ALGEBRA, by Solomon W. Golomb22. A PROOF OF SOME PROPERTIES OF REED-MULLER CODES BY MEANS OF THE NORMAL BASIS THEOREM, by Paul Camion23. 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 LinPART IV. FINITE GEOMETRIES25. CLASSIFICATION OF FINITE PROJECTIVE PLANES, by A. Barlotti26. TRANSLATION PLANES OF ORDER p2, by T. G. Ostrom27. CONSTRUCTION PROBLEMS OF FINITE PROJECTIVE PLANES, by R. H. Bruck28. CYCLICAL GENERATION OF LINEAR SUBSPACES IN FINITE GEOMETRIES, by C. Radhakrishna RaoPART V. GRAPHS29. SOME CLASSES OF PERFECT GRAPHS, by C. Berge30. A GEOMETRICAL VERSION OF THE FOUR COLOR PROBLEM, by W. T. Tutte31. EDGE COLORINGS IN BIPARTITE GRAPHS, by Jon Folkman and D. R. Fulkerson32. THE EIGENVALUES OF THE ADJACENCY MATRIX OF A GRAPH, by A. J. Hoffman33. LABELLING TO OBTAIN A MAXIMUM MATCHING, by M. L. BalinskiOriginally published in 1969.A UNC Press Enduring Edition - UNC Press Enduring Editions use the latest in digital technology to make available again books from our distinguished back