Results 231 to 240 of about 145,999 (267)
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Symmetric designs with bruck subdesigns
Combinatorica, 1982IfP is a finite projective plane of ordern with a proper subplaneQ of orderm which is not a Baer subplane, then a theorem of Bruck [Trans. AMS 78(1955), 464–481] asserts thatn≧m2+m. If the equalityn=m2+m were to occur thenP would be of composite order andQ should be called a Bruck subplane.
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Designs and Representation of the Symmetric Group
Designs, Codes and Cryptography, 2003A spectral characterization ``à la Delsarte'' is given for colored designs held by codes over non-binary alphabets. The tools include association schemes and also the representation theory of the symmetric group: tableaux, Specht modules, and zonal functions.
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A Technique for Constructing Symmetric Designs
Designs, Codes and Cryptography, 1998This important paper contains a new recursive construction method for symmetric designs which uses as ingredients balanced generalized weighing matrices and (the incidence matrices of) smaller symmetric designs. As an application of his general theory, the author obtains four infinite families of symmetric designs, three of which are entirely new ...
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Journal of Combinatorial Designs, 1999
For q, an odd prime power, we construct symmetric (2q^2+2q+1,q^2,1/2q(q+1)) designs having an automorphism group of order q that fixes 2q+1 points. The construction indicates that for each q the number of such designs that are pairwise non-isomorphic is very large.
Pavčević, Mario-O., Spence, Edward
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For q, an odd prime power, we construct symmetric (2q^2+2q+1,q^2,1/2q(q+1)) designs having an automorphism group of order q that fixes 2q+1 points. The construction indicates that for each q the number of such designs that are pairwise non-isomorphic is very large.
Pavčević, Mario-O., Spence, Edward
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Artifacts for Stamping Symmetric Designs
The American Mathematical Monthly, 2011It is well known that there are 17 crystallographic groups that determine the possible tessellations of the Euclidean plane. We approach them from an unusual point of view. Corresponding to each crystallographic group there is an orbifold. We show how to think of the orbifolds as artifacts that serve to create tessellations.
Hugh M. Hilden +3 more
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Half-regular symmetric designs [PDF]
Australas. J Comb., 1993 Suppose a symmetric 2-\((v,k, \lambda)\) design \(D\) has a group \(G\) of automorphisms of order \(v/2\) with two point orbits (each necessarily of length \(v/2)\). Such a \(G\) is called a half-regular group and the \(D\) on which it acts is called a half-regular symmetric design.
Alan Rahilly +3 more
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Quasi-affine symmetric designs
Designs, Codes and Cryptography, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sanjeevani Gharge, Sharad S. Sane
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1983
Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. 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 ...
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Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries. 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 ...
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Unitals and Unitary Polarities in Symmetric Designs
Designs, Codes and Cryptography, 1997A unital in a symmetric \(2\)-\((v,k,\lambda)\) design \({\mathcal D}\) is a subset \({\mathcal U}\) of the points such that through every \(P\) in \({\mathcal U}\) there are \(k-1\) blocks of \({\mathcal D}\) meeting \({\mathcal U}\) in \(\alpha\) points, for constant \(\alpha\), and one meeting \({\mathcal U}\) in \(P\). A polarity of \({\mathcal D}\)
Rudolf Mathon, Tran van Trung
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1997
Abstract In this chapter we look at symmetric designs, studying in particular Hadamard designs and finite projective planes. These are the ‘extreme’ symmetric designs in the sense of Theorem 3.1.2 below. For example, a (7,3,1) design is both a finite projective plane of order 2 and a Hadamard design of order 2; the lower and upper bounds
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Abstract In this chapter we look at symmetric designs, studying in particular Hadamard designs and finite projective planes. These are the ‘extreme’ symmetric designs in the sense of Theorem 3.1.2 below. For example, a (7,3,1) design is both a finite projective plane of order 2 and a Hadamard design of order 2; the lower and upper bounds
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