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Thursday, August 6, 2020 | History

8 edition of Quasi-symmetric designs found in the catalog.

Quasi-symmetric designs

by Mohan S. Shrikhande

  • 207 Want to read
  • 6 Currently reading

Published by Cambridge University Press in Cambridge [England], New York .
Written in English

    Subjects:
  • Block designs.,
  • Graph theory.,
  • Coding theory.

  • Edition Notes

    Includes bibliographical references (p. 207-221) and index.

    StatementMohan S. Shrikhande, Sharad S. Sane.
    SeriesLondon Mathematical Society lecture note series ;, 164
    ContributionsSane, Sharad S., 1950-
    Classifications
    LC ClassificationsQA166.3 .S57 1991
    The Physical Object
    Paginationxv, 225 p. :
    Number of Pages225
    ID Numbers
    Open LibraryOL2025959M
    ISBN 100521414075
    LC Control Number91000762

    Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs. Number Theory and Discrete Mathematics, () Non-symmetric nearly triply regular designs. Symmetric designs with the symmetric difference property are a special type of symmetric designs and related to Hadamard difference sets and a type of linear codes. Their derived and residual designs are quasi-symmetric and have a close connection with a family of .

    Although graph theory, design theory, and coding theory had their origins in various areas of applied mathematics, today they are to be found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, into an invaluable textbook. Symmetric and Quasi-Symmetric Designs and Strongly Regular Graphs Sharad S. Sane Department of Mathematics, University of Mumbai, Vidyanagari, Santacruz East, Mumbai, India.

    This is the concluding volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to . An infinite family of quasi-symmetric designs Aart Blokhuis Technical University Eindhoven and Free University Amsterdam and Willem H. Haemers Tilburg University Quasi-symmetric designs, Chapter 37 in The CRC Hand-book of Combinatorial Designs (C.J. Colbourn and J.H. Dinitz eds.), CRC Press, , pp.


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Quasi-symmetric designs by Mohan S. Shrikhande Download PDF EPUB FB2

Extensions of symmetric designs --VIII. Quasi-symmetric 2-designs --IX. Towards a classification of quasi-symmetric 3-designs --X.

Codes and quasi-symmetric designs --References --Index. Series Title: London Mathematical Society lecture note series.

Basic results on quasi-symmetric designs; 4. Some configurations related to strongly regular graphs and quasi-symmetric designs; 5. Strongly regular graphs with strongly regular decompositions; 6. The Witt designs; 7.

Extensions of symmetric designs; 8. Quasi-symmetric 2-designs; 9. Towards a classifications of quasi-symmetric 3-designs; Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry. In this book the authors discuss the generalization of results and applications to quasi-symmetric designs.

Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry.

In this book the authors discuss the generalization of results and applications to quasi-symmetric designs. Quasi-symmetric designs are closely related to symmetric designs. Algebraic coding theory has in recent years been increasingly applied to the study of combinatorial designs. This book gives.

A quasi-symmetric design (QSD) is a (v,k,λ) design with two intersection numbers x,y, where 0≤x. The paper studies quasi-symmetric 2-(64, 24, 46) designs supported by minimum weight codewords in the dual code of the binary code spanned by the lines of AG(3, 22).

1. Introduction. A t-(v, k, λ) design is a set Quasi-symmetric designs book v points together with a collection of k-element subsets called blocks such that every t-subset of points is contained in exactly λ blocks.

The design is quasi-symmetric if any two blocks intersect either in x or in y points, for non-negative integers x. This book presents some of the algebraic techniques that have been brought to bear on the question of existence, construction and symmetry of symmetric designs – including methods inspired by the algebraic theory of coding and by the representation theory of finite groups – and includes many results.

A t-(v,k,λ) design D is quasi-symmetric with intersection numbers x and y (x designs naturally arise in the investigation of the duals of designs with λ = 1. A non-symmetric (b > v) 2-(v,k,1) design is quasisymmetric with x = 0 and y = 1.

A quasi-symmetric design (QSD) is a 2-(v, k, lambda) design with intersection numbers x and y with x design is formed on its blocks with two distinct blocks being. JOURNAL OF COMBINATORIAL THEORY 9, () NOTE A Note on Quasi-symmetric Designs W.

WALLIS La Trobe University, Bundoora, VictoriaAustralia Communicated by Mark Kac Received October 9, A quasi-symmetric balanced incomplete block design with parameters (4y, 8y -- 2, 4y -- l, 2y, 2y ) exists if and only if there is an Hadamard matrix.

Quasi-symmetric designs are block designs for which the block intersection numbers take two distinct values. There are many solved and unsolved conjectures and questions associated with such. A quasi-symmetric t-design is a t-design with two block intersection sizes p and q (where $p Quasi-symmetric 3-designs are classified with $p = 1$.

The only. Quasi-symmetric designs with intersection numbers x > 0 and y = x + 2 under the condition λ > 1 are investigated. If D(v, b, r, k, λ; x, y) is a quasi-symmetric design with above conditions then it is shown that either λ = x + 1 or x + 2 or D is a design with the parameters given in the Table 6 or complement of one of these designs.

Neumaier, A. Regular sets and quasi-symmetric 2-designs, in Combinatorics and Graph Theory (D. Jungnickel and K. Vedder, eds.). Lecture Notes in Mathematics, New York/Berlin: Springer-Verlag, pp. – Google Scholar. Computational techniques for the construction of quasi-symmetric block designs are explored and applied to the case with $ 56 $ points.

One new $ (56,16,18) $ and many new $ (56,16,6) $ designs are discovered, and non-existence of $ (56,12,9) $ and $ (56,20,19) $ designs with certain automorphism groups is proved. Abstract. Quasi-symmetric designs are block designs with two block intersection numbersx andy It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block sizek, there are finitely many such finiteness results on block graphs are derived.

For a quasi-symmetric 3-design with positivex andy, the intersection numbers are shown to be roots of a quadratic whose. A. NeumaierRegular sets and quasi-symmetric designs D. Jungnickel, K. Vedder (Eds.), Combinatorial Theory, Lect. Notes in Math. Quasi-symmetric designs are closely related to symmetric designs.

These are designs that have (at the most) two block intersection numbers. One can associate a block graph with a quasi-symmetric design and in many cases of interest, this also turns out to be a graph with special properties, and is called a strongly regular graph.

JOURNAL OF COMBINATORIAL THEORY, Series A 59, () On Symmetric and Quasi-Symmetric Designs with the Symmetric Difference Property and Their Codes DIETER JUNGNICKEL AND VLADIMIR D. TONCHEV Justus-Liebig-University, Giessen, Germanv Communicated by J. H. van Lint Received Decem DEDICATED TO PROFESSOR .The design is quasi-symmetric if any two blocks intersect either in x or in y points, for non-negative integers x quasi-symmetric designs, and to [2] for designs in general.

It is known that there are no quasi-symmetric designs for t ‚ 5, and. Quasi-symmetric triangle-free designs D with block intersection numbers 0 and y and with no three mutually disjoint blocks are studied.

It is shown that the parameters of D are expressible in terms of only two parameters y and m, where m = k/y, k being the block size. Baartmans and Shrikhande proved that 2 ⩽ m ⩽ y + 1 and characterized the extremal values of m.