2023年8月28日，英国Strathclyde大学Sergey Kitaev教授应邀访问组合数学中心，并作了题为“Naturally labelled posets and a hierarchy related to interval orders”的学术报告，并与组合中心师生进行了热烈的交流讨论。
报告摘要：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. Restricting naturally labelled posets (considering (2+2)-free, k-free, 3+1-free, N-free, etc, posets) we obtain combinatorial objects fitting nicely to a hierarchy related to interval orders that involves, for example, Fishburn matrices, factorial posets, ascent sequences, pattern-avoiding permutations, and many more objects. 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 the objects in question, and will discuss the hierarchy along with open (embedding) problems.
This is joint work with David Bevan and Gi-Sang Cheon.