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S-Quasi-symmetry by Lowell A. Carmony; Soon Teck Tan is a Computer Science article available to read on EtoBox.

What is S-Quasi-symmetry about?

A (u, b, r, k, A) block design lid is a pair (!?,a) sucl\_ that (a) PI=Q (b) for each B E 3, IBi= k, (c) for each distinct pair of points X, y in 9 there are exactly A blocks B in @ with X, y E B, and, as is well known, (d) b=I@\=ur,'k, (e) r = the number of blocks' through any point = h(u -l)/(k -1). We, of course, exclude the trivial designs where all subsets of 9 of size k are chosen as blocks. The design is symmetric if v = b or equivalently if any two blocks intersect in A points. A design 9 is quasi-symmetric if there are exactly two block intelsection numbers, x and y (X < y ). Let B. lx a block 'and consider all intersections B f3 B. for B ~58. Let Q and a' be the frequencies of the intersection numbers y and x respectively. (It is easy to see that these are independent of BO. See (1) belowj. Follciwing [4& $3. is s-quasi-symmetric if it is quasi-symmetric and s = min{cr, a$ The purpose of this paper is to present an algorithm that for given s determines the par&me ters of all potential s-quasisymmetrrr: designs. Using simple counting arguments, as suggested in $1, we obtain the fundamental relations: (1) (2) Every quasi-symmetric design is sbquasi-symmetric for some .s <$(

Who reads S-Quasi-symmetry?

Author

Lowell A. Carmony; Soon Teck Tan

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0012-365X)

Published

1981

Language

LA

Field

Computer Science (Physical Sciences)