报告题目1：On the distribution of Random Strict $(n, dn\pm 1)$-Core Partitions

报告人：熊欢教授，哈尔滨工业大学

报告时间：2025年11月12日（周三）9:30

报告地点：腾讯会议：159715841

报告摘要：Amdeberhan's conjectures concerning the enumeration, average size, and largest size of strict $(n,n+1)$-core partitions have stimulated extensive research in this area. Nevertheless, the investigation of random core partitions remains relatively underdeveloped. In this talk, we first present several polynomiality results and asymptotic formulas for the moments of sizes of random strict $(n, dn\pm 1)$-core partitions. We further establish the asymptotic normality of their sizes. Analogous results are also derived for random (strict) $n$-core partitions and random self-conjugate $n$-core partitions with bounded perimeter—that is, bounded largest hook length. These findings resolve several conjectures posed by Zaleski and stand in contrast to the asymptotic behavior derived by Even-Zohar (2022) for the size of a random $(s,t)$-core partition with coprime $s$ and $t$, which converges in distribution to Watson’s $U^2$ distribution. These are joint works with Wenston J.T. Zang, Yetong Sha, and Jiange Li.

报告人简介：熊欢，哈尔滨工业大学数学研究院教授/科研副院长。研究方向为代数组合和机器学习。在TPAMI, JMLR, IJCV, JCTA, Sci. China Math., ICML, ICLR, NeurIPS, NBER等国际知名期刊和顶级会议发表论文50余篇，被引用次数2000多次。主持或参与瑞士国家自然科学基金、法国国家科研中心的多项研究项目。入选2024年“小米青年学者”。自2024年起担任中国工业与应用数学学会图论组合及应用专委会委员。担任人工智能国际顶级会议ICLR 2026领域主席。

报告题目2：Counting alternating runs via Hetyei-Reiner trees

报告人：潘琼琼副教授，温州大学

报告时间：2025年11月12日（周三）9:30

报告地点：腾讯会议：159715841

报告摘要：The generating polynomial of all $n$--permutations with respect to the number of alternating runs possesses a root at $-1$ of multiplicity $\lfloor (n-2)/2\rfloor$ for  n\ge2$. This fact can be deduced by combining the David--Barton formula for Eulerian polynomials with the Foata--Schützenberger  gamma--decomposition of these polynomials. Recently, Bóna provided a group--action proof of this result. In this talk, I propose an alternative approach based on the Hetyei--Reiner action on binary trees, which yields a new combinatorial interpretation of Bóna’s quotient polynomial. Furthermore, we extend our study to analogous results for permutations of types~B and~D. As a consequence of our bijective framework, we also obtain combinatorial proofs of David--Barton type identities for permutations of types~A and~B. This talk is based on a joint work with Yunze Wang and Jiang Zeng.

报告人简介：潘琼琼，2020年博士毕业于法国里昂大学，2021年入职温州大学，主要研究计数组合学以及正交多项式理论。多篇论文发表在JCTA、AAM、DM、EJC等组合数学领域国际期刊上，目前主持一项国家自然科学基金青年项目。

邀请人：离散数学研究所