Annals of Combinatorics 1 (1997) 227-243
On the Maximum Number of Fixed Points in Automorphisms of Prime Order of 2-(v,k,1) Designs
D.L. Kreher, D.R. Stinson, and L. Zhu
Department of Mathematical Sciences, Michigan Technological
University Houghton, MI 49931,
Computer Science and Engineering Department, University of Nebraska Lincoln, NE 68588, USA
Department of Mathematics, Suzhou University, Suzhou 215006, P.R. China
Received January 15, 1997
AMS Subject Classification: 05B05
Abstract. In this paper, we study 2-(v,k,1) designs with automorphisms of prime order p, having the maximum possible number of fixed points. We prove an upper bound on the number of fixed points, and we study the structure of designs in which this bound is met with equality (such a design is called a p-MFP(v,k)). Several characterizations and asymptotic existence results for p-MFP(v,k) are obtained. For (p,k) = (3,3), (5,5), (2,3) and (3,4), necessary and sufficient conditions on v are obtained for the existence of a p-MFP(v,k). Further, for 3 $\leq$ k $\leq$ 5 and for any prime p$\equiv$ mod k(k-1), we establish necessary and sufficient conditions on v for the existence of a p-MFP(v,k).
Keywords: 2-design, automorphism, fixed point
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