On balanced complementation for regular t-wise balanced designs

AbstractVanstone has shown a procedure, called r-complementation, to construct a regular pairwise balanced design from an existing regular pairwise balanced design. In this paper, we give a generalization of r-complementation, called balanced complementation. Necessary and sufficient conditions for balanced complementation which gives a regular t-wise balanced design from an existing regular t-wise balanced design are shown. We characterize those aspects of designs which permit balanced complementation. Results obtained here will be applied to construct regular t-wise balanced designs which are useful in Statistics

International Journal of Mathematical Combinatorics, Vol.7A

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

On the primarity of some block intersection graphs

Philosophiae Doctor - PhDA tactical con guration consists of a nite set V of points, a nite set B of blocks and an incidence relation between them, so that all blocks are incident with the same number k points, and all points are incident with the same number r of blocks (See [14] for example ). If v := jV j and b := jBj; then v; k; b; r are known as the parameters of the con guration. Counting incident point-block pairs, one sees that vr = bk: In this thesis, we generalize tactical con gurations on Steiner triple systems obtained from projective geometry. Our objects are subgeometries as blocks. These subgeometries are collected into systems and we study them as designs and graphs. Considered recursively is a further tactical con guration on some of the designs obtained and in what follows, we obtain similar structures as the Steiner triple systems from projective geometry. We also study these subgeometries as factorizations and examine the automorphism group of the new structures. These tactical con gurations at rst sight do not form interesting structures. However, as will be shown, they o er some level of intriguing symmetries. It will be shown that they inherit the automorphism group of the parent geometry

Corpus linguistics: A guide to the methodology

Corpora are widely used in linguistics, but not always wisely. This book attempts to frame corpus linguistics systematically as a variant of the observational method. The first part introduces the reader to the general methodological discussions surrounding corpus data as well as the practice of doing corpus linguistics, including issues such as the scientific research cycle, research design, extraction of corpus data and statistical evaluation. The second part consists of a number of case studies from the main areas of corpus linguistics (lexical associations, morphology, grammar, text and metaphor), surveying the range of issues studied in corpus linguistics while at the same time showing how they fit into the methodology outlined in the first part

Corpus linguistics: A guide to the methodology

Corpora are widely used in linguistics, but not always wisely. This book attempts to frame corpus linguistics systematically as a variant of the observational method. The first part introduces the reader to the general methodological discussions surrounding corpus data as well as the practice of doing corpus linguistics, including issues such as the scientific research cycle, research design, extraction of corpus data and statistical evaluation. The second part consists of a number of case studies from the main areas of corpus linguistics (lexical associations, morphology, grammar, text and metaphor), surveying the range of issues studied in corpus linguistics while at the same time showing how they fit into the methodology outlined in the first part