Quasi-affine symmetric designs

Gharge, Sanjeevani ; Sane, Sharad (2007) Quasi-affine symmetric designs Designs, Codes and Cryptography, 42 (2). pp. 145-166. ISSN 0925-1022

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Official URL: http://www.springerlink.com/content/d743n267u22137...

Related URL: http://dx.doi.org/10.1007/s10623-006-9027-4


A symmetric design with parameters v = q2(q + 2), k = q(q + 1), λ = q, q ≥ 2, is called a quasi-affine design if its point set can be partitioned into q + 2 subsets P0, P1,..., Pq, Pq+1 such that the induced structure in every point neighborhood is an affine plane of order q (repeated q times). A quasi-affine design with q ≥ 3 determines its point neighborhoods uniquely and dual of such a design is also a quasi-affine design. These structural properties pave way for definition of a strongly quasi-affine design and it is also shown that associated with every quasi-affine design is a unique strongly quasi-affine design from which the given quasi-affine design is obtained by certain unique cutting and pasting operation. This investigation also enables us to associate a unique 2-regular graph with q + 2 vertices and in turn, a unique colored partition of the integer q + 2. These combinatorial consequences are finally used to obtain an exponential lower bound on the number of non-isomorphic solutions of such symmetric designs improving the earlier lower bound of 2.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Symmetric Designs; Affine Planes; Latin Squares; Coloured Partitions; Non-isomorphic Designs
ID Code:68022
Deposited On:02 Nov 2011 03:12
Last Modified:02 Nov 2011 03:12

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