报告时间：2022年5月19日（星期四）14:00-

报告地点：腾讯会议ID：250-571-357

报 告 人：傅士硕 教授

工作单位：重庆大学

举办单位：数学学院

报告简介：

Given a general multiset $\M=\{1^{m_1},2^{m_2},\ldots,n^{m_n}\}$, where $i$ appears $m_i$ times, a multipermutation $\pi$ of $\M$ is called “quasi-Stirling”, if it contains no subword of the form $abab$ with $a\neq b$. We designate exactly one entry of $\pi$, say $k\in \M$, which is not the leftmost entry among all entries with the same value, by underlining it in $\pi$, and we refer to the pair $(\pi,k)$ as a quasi-Stirling multipermutation of $\M$ rooted at $k$. In this talk, we introduce certain vertex and edge labeled trees and give a new bijective proof of an identity due to Yan, Yang, Huang and Zhu, which links the enumerator of rooted quasi-Stirling multipermutations by the numbers of ascents, descents, and plateaus, with the exponential generating function of the bivariate Eulerian polynomials. This identity and our bijective approach to proving it enables us to

1) prove bijectively a Carlitz type identity involving quasi-Stirling polynomials on multisets that was first obtained by Yan and Zhu.

2) confirm a recent partial $\gamma$-positivity conjecture due to Lin, Ma and Zhang, and find a combinatorial interpretation of the $\gamma$-coefficients in terms of two new statistics defined on quasi-Stirling multipermutations called sibling descents and double sibling descents.

The talk is based on joint work with Yanlin Li.

报告人简介：

傅士硕，教授，博士生导师，2011年博士毕业于宾夕法尼亚州立大学，2011-2012在韩国科学技术院（KAIST）做博士后研究。研究兴趣主要为组合数学中的整数分拆理论、排列统计量同分布问题以及组合序列的伽马非负性等。已在J. Combin. Theory Ser. A, Adv. Appl. Math., SIAM Disc. Math., European J. Combin., Ramanujan J., J. Number Theory 等杂志发表论文30余篇，多次受邀参加国际国内学术会议并作邀请报告，获批国家自然科学基金两项。现任中国工业与应用数学学会图论组合及应用专业委员会副秘书长、中国运筹学会图论组合学分会理事、重庆市运筹学会常务理事。