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## 第94回 2019年8月2日 15:00〜16:30

Jon Xu（東北大学）「A survey of Erdős-Ko-Rado type theorems」

Consider a family of subsets of $\{1,2,\dots, n\}$, each subset of size $k$, such that they have pairwise non-empty intersection. The Erdős-Ko-Rado theorem describes the maximum size of such a family, and the structure of these maximal families. The theorem extended to many other mathematical objects that have a notion of intersection, including vector spaces, permutations, and buildings.

In this talk, I will outline the original Erdős-Ko-Rado theorem, and the vector space version. Then, I will discuss the recent work of Ihringer-Metsch-Mühlherr ['An EKR-theorem for finite buildings of type $D_{\ell}$', Journal of Algebraic Combinatorics, 2017] on developing an Erdős-Ko-Rado theorem for finite buildings.