Speaker: Sergey Kitaev, professor, University of Strathclyde, UK

Date: June 8, 2025

Time: 9:30-11:00 am

Location: E119, Huagang East Building, Shandong University Qingdao Campus

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences, Shandong University

Abstract:

A partially ordered set (poset) (P, <_P) isnaturally 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 calledposet 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.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/203077.htm