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