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(xué)
舉辦單位：數(shù)學(xué)學(xué)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(dǎo)師，2011年博士畢業(yè)于賓夕法尼亞州立大學(xué)，2011-2012在韓國科學(xué)技術(shù)院（KAIST）做博士后研究，2012年入職重慶大學(xué)。研究興趣主要為組合數(shù)學(xué)中的整數(shù)分拆理論、排列統(tǒng)計量同分布問題以及組合序列的伽馬非負(fù)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(fā)表論文30余篇，多次受邀參加國際國內(nèi)學(xué)術(shù)會議并作邀請報告，獲批國家自然科學(xué)基金兩項(xiàng)?，F(xiàn)任中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會圖論組合及應(yīng)用專業(yè)委員會副秘書長、中國運(yùn)籌學(xué)會圖論組合學(xué)分會理事、重慶市運(yùn)籌學(xué)會常務(wù)理事。
