报告题目：Complete non-ambiguous trees, associated permutations, and the Abelian sandpile model

报告人： Thomas Selig 博士，西交利物浦大学

报告时间：2023年5月17日 10：00-11: 30

报告地点：23-220

报告摘要：We study a link between complete non-ambiguous trees (CNATs) and permutations exhibited by Daniel Chen and Sebastian Ohlig in recent work. In this, they associate a certain permutation to the leaves of a CNAT, and show that the number of $n$-permutations that are associated with exactly one CNAT is $2^{n-2}$. We connect this to work by the first author and co-authors linking complete non-ambiguous trees and the Abelian sandpile model. This allows us to prove a number of conjectures by Chen and Ohlig on the number of $n$-permutations that are associated with exactly $k$ CNATs for various $k > 1$, via various bijective correspondences between such permutations. We also exhibit a new bijection between $(n-1)$-permutations and CNATs whose permutation is the decreasing permutation $n(n-1)\cdots1$. This bijection maps the left-to-right minima of the permutation to dots on the bottom row of the corresponding CNAT, and descents of the permutation to empty rows of the CNAT.

 报告人简介：Thomas Selig 博士，西交利物浦大学助理教授，研究兴趣包括枚举和双射组合数学，离散概率，沙堆模型之间的相互作用（包括阿贝尔沙堆模型和随机变量）以及来自组合学、统计物理学等的其他对象，在JCTA， EuJC等组合数学权威刊物上发表学术论文多篇。