Designs, permutations, and transitive groups

作     者：Shi, Minjia Li, XiaoXiao Solé, Patrick 

作者机构：Key Laboratory of Intelligent Computing & Signal Processing of Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China I2M Aix-Marseille Univ. Centrale Marseille CNRS Marseille France 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2021年

核心收录：

主　　题：Method of moments 

摘      要：A notion of t-designs in the symmetric group on n letters, called permutation designs in this paper, was introduced by Godsil in 1988. In particular t-transitive sets of permutations form a t-design in that sense. We derive special lower bounds for t = 1 and t = 2 by a power moment method. For general n, t we give a a lower bound on the size of such t-designs of n(n − 1) . . . (n − t + 1), which is best possible when sharply t-transitive sets of permutations exist. This shows, in particular, that tight 2-designs do not *** Codes Primary 05E35, Secondary O5E20, 05E24 © 2021, CC BY.