報告時間：2022年5月19日（星期四）14:00
報告平臺：騰訊會議 ID:250 571 357
報 告 人：傅士碩 教授
工作單位：重慶大學
舉辦單位：數學學院
報告簡介：
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.
報告人簡介：
傅士碩，教授，博士生導師，2011年博士畢業于賓夕法尼亞州立大學，2011-2012在韓國科學技術院（KAIST）做博士后研究，2012年入職重慶大學。研究興趣主要為組合數學中的整數分拆理論、排列統計量同分布問題以及組合序列的伽馬非負性等。已在J. Combin. Theory Ser. A, Adv. Appl. Math., SIAM Disc. Math., European J. Combin., Ramanujan J., J. Number Theory 等雜志發表論文30余篇，多次受邀參加國際國內學術會議并作邀請報告，獲批國家自然科學基金兩項。現任中國工業與應用數學學會圖論組合及應用專業委員會副秘書長、中國運籌學會圖論組合學分會理事、重慶市運籌學會常務理事。
