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Combinatorial Design Theory

1st Edition
Volume 34
September 22, 2011
C.J. Colbourn + 1 more
English
Paperback
9 7 8 0 4 4 4 5 5 7 0 2 5
eBook
9 7 8 0 0 8 0 8 7 2 6 0 5

Combinatorial design theory is a vibrant area of combinatorics, connecting graph theory, number theory, geometry, and algebra with applications in experimental design, coding theory, and numerous applications in computer science.This volume is a collection of forty-one state-of-the-art research articles spanning all of combinatorial design theory. The articles develop new methods for the construction and analysis of designs and related combinatorial configurations; both new theoretical methods, and new computational tools and results, are presented. In particular, they extend the current state of knowledge on Steiner systems, Latin squares, one-factorizations, block designs, graph designs, packings and coverings, and develop recursive and direct constructions.The contributions form an overview of the current diversity of themes in design theory for those peripherally interested, while researchers in the field will find it to be a major collection of research advances. The volume is dedicated to Alex Rosa, who has played a major role in fostering and developing combinatorial design theory.

Random Graphs '85

1st Edition
Volume 33
September 22, 2011
M. Karonski + 1 more
English
Paperback
9 7 8 0 4 4 4 5 5 6 9 9 8
eBook
9 7 8 0 0 8 0 8 7 2 5 5 1

Covering a wide range of Random Graphs subjects, this volume examines series-parallel networks, properties of random subgraphs of the n-cube, random binary and recursive trees, random digraphs, induced subgraphs and spanning trees in random graphs as well as matchings, hamiltonian cycles and closure in such structures. Papers in this collection also illustrate various aspects of percolation theory and its applications, properties of random lattices and random walks on such graphs, random allocation schemes, pseudo-random graphs and reliability of planar networks. Several open problems that were presented during a special session at the Seminar are also included at the end of the volume.

Group and Semigroup Rings

1st Edition
Volume 126
September 22, 2011
G. Karpilovsky
English
eBook
9 7 8 0 0 8 0 8 7 2 3 7 7

A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.

Combinatorics '86

1st Edition
Volume 37
September 22, 2011
M. Marchi + 2 more
English
Paperback
9 7 8 0 4 4 4 5 5 7 0 6 3
eBook
9 7 8 0 0 8 0 8 6 7 7 7 9

Recent developments in all aspects of combinatorial and incidence geometry are covered in this volume, including their links with the foundations of geometry, graph theory and algebraic structures, and the applications to coding theory and computer science.Topics covered include Galois geometries, blocking sets, affine and projective planes, incidence structures and their automorphism groups. Matroids, graph theory and designs are also treated, along with weak algebraic structures such as near-rings, near-fields, quasi-groups, loops, hypergroups etc., and permutation sets and groups.The vitality of combinatorics today lies in its important interactions with computer science. The problems which arise are of a varied nature and suitable techniques to deal with them have to be devised for each situation; one of the special features of combinatorics is the often sporadic nature of solutions, stemming from its links with number theory. The branches of combinatorics are many and various, and all of them are represented in the 56 papers in this volume.