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One-factors and the existence of affine designs

✍ Scribed by Neal Brand; Somporn Sutinuntopas

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 582 KB
Volume: 120
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90562-8

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✦ Synopsis

One-factors and the existence of affine designs, Discrete Mathematics 120 (1993) 25-35. Kiihler (1982) defines a graph G, for p a prime which he relates to affine designs. He shows that if the graph has a l-factor then there exists an affine 3-(p, 4, %) design with 1, satisfying the usual necessary conditions. Here we generalize Kiihler's results to include finite fields. M= ~ BiUi i=l in Q(A) is called a multiset over A, and pi is the multiplicity of Ui in M. If each Ui has the same multiplicity 2 in M, we may write M = ,%A. Let V be a v-set and Y be any positive integer less than u. We denote the collection of all r-subsets of V by (I', r). Definition 1.1. The multiset g =Cr= 1 fi<Bi over the set (V, k) is a t-(u, k, 2) design if

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