On the maximum number of fixed points in automorphisms of prime order of 2-(v,k,1) designs |
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Authors: | D L Kreher D R Stinson L Zhu |
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Institution: | (1) Department of Mathematical Sciences, Michigan Technological University, 49931 Houghton, MI, USA;(2) Computer Science and Engineering Department, University of Nebraska, 68588 Lincoln, NE, USA;(3) Department of Mathematics, Suzhou University, 215006 Suzhou, P.R. China |
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Abstract: | In this paper, we study 2-(v, k, 1) designs with automorphisms of prime orderp, 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 ap-MFP(v, k)). Several characterizations and asymptotic existence results forp-MFP(v, k) are obtained. For (p, k)=(3,3), (5,5), (2,3) and (3,4), necessary and sufficient conditions onv are obtained for the existence of ap-MFP(v, k). Further, for 3≤k≤5 and for any primep≡1 modk(k−1), we establish necessary and sufficient conditions onv for the existence of ap-MFP(v, k). |
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Keywords: | 05B05 |
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