Corpus ID: 118355962

Contemporary design theory : a collection of surveys

  title={Contemporary design theory : a collection of surveys},
  author={J. Dinitz and D. Stinson},
Orthogonal Factorizations of Graphs (B. Alspach, et al.). Conjugate--Orthogonal Latin Squares and Related Structures (F. Bennett & L. Zhu). Directed and Mendelsohn Triple Systems (C. Colbourn & A. Rosa). Room Squares and Related Designs (J. Dinitz & D. Stinson). Steiner Quadruple Systems (A. Hartman & K. Phelps). Difference Sets (D. Jungnickel). Decomposition Into Cycles II: Cycle Systems (C. Lindner & C. Rodger). Coverings and Packings (W. Mills & R. Mullin). Colorings of Block Designs (A… Expand
Rank Inequalities for Packing Designs and Sparse Triple Systems
Sparseness inequalities are proven to induce facets for the sparse PSTS polytope; some extremal families of PSTS known as Erdos configurations play a central role in this proof. Expand
Generalized packing designs
A related class of combinatorial designs which simultaneously generalize packing designs and packing arrays is defined and methods for constructing maximum generalized packings with t = 2 and block size k = 3 or 4 are provided. Expand
Equitable colourings in the Witt designs
Equitable colourings of Steiner triple systems, five Witt systems based on the Mathieu groups, and a thorough analysis of blocking sets of these designs are studied. Expand
A Technique for Constructing Symmetric Designs
  • Yury J. Ionin
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1998
A sufficient condition is given for the matrix W⊗ M, where Mε M and W is a balanced generalized weighing matrix over G, to be the incidence matrix of a larger symmetric design. Expand
Block transitive resolutions of t-designs and room rectangles
Abstract By a resolution of t-designs we mean a partition of the trivial design ( X k ) of all k-subsets of a v-set X into t − (v′,k,λ) designs, where v′ ⩽ v. A resolution of t-designs with v = v′ isExpand
Randomly orthogonal factorizations with constraints in bipartite networks
It is shown that every bipartite ( 0, m f − ( m − 1 ) r -graph G has a (0, f )-factorization randomly r -orthogonal to n vertex disjoint mr -subgraphs of G in certain conditions. Expand
A Note on Difference Sets
LetDbe a (v,k,?)-difference set in a groupG. Assume thatGhas a normal subgroupNsuch thatG/Nis cyclic or nearly cyclic. Under the self-conjugacy assumption on exp(G/N), we shall give bounds on |N|Expand
Building Symmetric Designs With Building Sets
  • Yury J. Ionin
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1999
We introduce a uniform technique for constructing a family of symmetric designs with parameters (v(qm+1-1)/(q-1), kqm,λqm), where m is any positive integer, (v, k, λ) are parameters of an abelianExpand
Cocyclic Orthogonal Designs and the Asymptotic Existence of Cocyclic Hadamard Matrices and Maximal Size Relative Difference Sets with Forbidden Subgroup of Size 2
It is proved there is a cocyclic Hadamard matrix of order 2ts for any odd integer s>1 and any t??8log2s? and there is an algebraic procedure for constructing and classifying these designs when each indeterminate is constrained to appear just once in each row and column of the orthogonal designs. Expand
On nesting of G-decompositions of ?- K v where G has four nonisolated vertices or less
The complete multigraph λKv is said to have a G-decomposition if it is the union of edge disjoint subgraphs ofKv each of them isomorphic to a fixed graph G. The spectrum problem forG-decompositionsofExpand