Some designs from the fixed points of alternating groups

	Some designs from the fixed points of alternating groups
Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 30 بهمن 1403 اصل مقاله (471.59 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.141435.2178
نویسندگان
Madimetja Jan Kekana^* ¹؛ Amin Saeidi²؛ Thekiso Seretlo³
¹Department of Mathematics and Applied Mathematics, Faculty of Science and Agriculture, University of Limpopo, South Africa.
²Department of mathematics and Applied Mathematics, University of Limpopo, South Africa.
³Department of Pure and Applied Analytics, North West University, mafikeng Campus, Mmabatho, South Africa.
چکیده
In this paper, we construct some $1-(v,k,\lambda)$ designs from the alternating group $G=A_{n}$ with the maximal subgroup isomorphic to $M=A_{n-1}$. The method we use is called Key-Moori Method $2$. Furthermore, from the set $I_x$ which is the intersection of all blocks containing the point $x\in G$, we construct corresponding reduced designs. Our aim is to give explicit formulae to compute the parameters of the designs based on the cyclic structures of the permutations in $G$.
کلیدواژه‌ها
Alternating groups؛ Reduced designs؛ Key-Moori Methods

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