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.

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 ?=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