Induced designs and fixed points

作者：Chen, Jianfu; Zhou, Shenglin^*

来源：Discrete Mathematics, 2021, 344(3): 112242.

DOI：10.1016/j.disc.2020.112242

• 2-design
• Induced design
• Automorphism group
• Fixed point

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 FixH. We extend the work of A.R. Camina and J. Siemons and we also state that if there is an induced design on FixH, then vertical bar FixH vertical bar <= 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 FixH with vertical bar FixH vertical bar > r and block size k(0).