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On block-transitive \(3\)-\((v,k,1)\) designs

尹富纲 Fugang Yin

Central South University (中南大学)

Time: 16:00-17:00 (GMT+8), Tuesday November 21st, 2023
Location: Zoom

Abstract: A \(t\)-\((v,k,\lambda)\) design \(\mathcal{D}= (\mathcal{P},\mathcal{B})\) is an incidence structure consisting of a set \(\mathcal{P}\) of \(v\) points and a set \(\mathcal{B}\) of \(k\)-subsets of \(\mathcal{P}\) called blocks such that, each block in \(\mathcal{B}\) has size \(k\), and each \(t\)-subset of \(\mathcal{P}\) lies in exactly \(\lambda\) blocks from \(\mathcal{B}\). Those \(t\)-\((v,k,1)\) designs are also called Steiner \(t\)-designs. An automorphism of the design \(\mathcal{D}\) is a permutation on its point set that also permutes the blocks among themselves. We say that \(\mathcal{D}\) is \(G\)-block-transitive if \(G\) is a subgroup of the full automorphism group of \(\mathcal{D}\) and acts transitively on the block set. In this talk, I will discuss some idea on studying block-transitive Steiner \(3\)-designs, and some classification results of such designs. Joint work with Weijun Liu and Ting Lan.

Host: 黄弘毅 Hong Yi Huang