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Induced designs and fixed points
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.disc.2020.112242
Jianfu Chen , Shenglin Zhou

Abstract Let D be a 2- ( v , k , 1 ) design and H be an automorphism group of D . This paper studies the induced design on the fixed points of H , denoted by Fix H . We extend the work of A.R. Camina and J. Siemons and we also state that if there is an induced design on Fix H , then | Fix H | ≤ r in most cases, where r is the number of blocks containing a given point. Moreover, for a given k 0 , there exist only finitely many designs admitting an induced design on Fix H with | Fix H | > r and block size k 0 .

中文翻译:

诱导设计和固定点

摘要 令 D 为 2- ( v , k , 1 ) 设计,H 为 D 的自同构群。本文研究了 H 不动点上的诱导设计,记为 Fix H 。我们扩展了 AR Camina 和 J.Siemons 的工作,并且我们还声明,如果在 Fix H 上存在诱导设计,那么 | 修复 H | ≤ r 在大多数情况下,其中 r 是包含给定点的块数。此外,对于给定的 k 0 ,只有有限多个设计允许在 Fix H 上使用 | 进行诱导设计。修复 H | > r 和块大小 k 0 。
更新日期:2021-03-01
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