报告人：Sergey Kitaev 教授（University of Strathclyde,UK）

时间：2025年03月27日 10:30-

地点：理科楼LA103

摘要：A partially ordered set (poset) (P,<_P) is naturally labelled by numbers in {1,2,...,n} if x <_P y implies x<y.  Naturally labelled posets are in one-to-one correspondence with certain lower triangular binary matrices called poset matrices.

         By restricting naturally labelled posets – such as considering (2+2)-free, k-free, (3+1)-free, N-free, and similar classes of posets – we obtain combinatorial objects that fit nicely into a hierarchy related to interval orders. This hierarchy includes, for example, Fishburn matrices, factorial posets, ascent sequences, pattern-avoiding permutations, and many other structures. In particular, it turns out that (2+2,3)-free naturally labelled posets are in one-to-one correspondence with permutations avoiding the vincular pattern 12-34.

       In my presentation, I will introduce these objects and discuss the hierarchy, along with open (embedding) problems.  

       This is joint work with David Bevan and Gi-Sang Cheon.

邀请人: 傅士硕

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