Some designs from the fixed points of alternating groups

	Some designs from the fixed points of alternating groups
Transactions on Combinatorics
دوره 15، شماره 1، خرداد 2026، صفحه 47-54 اصل مقاله (494.98 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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