报告题目： Bijective proofs of several conjectures on Jacobi permutations

摘要：Jacobi permutations,   invented  by Viennot in the context of  the Jacobi elliptic functions, are  counted by the Euler numbers.  Recently, Henke, Hoffman, Stephens, Yuan, and Zhuang studied refined enumerations of Jacobi permutations and proposed three conjectures concerning the distribution of several statistics  on  Jacobi permutations. In this paper, we prove these conjectures by establishing explicit bijections involving  increasing even trees,  increasing binary trees, alternating permutations, and André permutations.   One highlight of our results is  a bijection between Jacobi permutations and André I permutations that transforms the pair of statistics  $(\Ascbot, \last)$ to  the pair of statistics $(\Desbot, \first)$. Here  the statistic $\Ascbot$ (resp., $\Desbot$) denotes the set of ascent bottoms (resp., descent bottoms) of permutations,  and the statistic $\first$ (resp., $\last$) denotes the first (resp., $\last$) letter of  permutations.  Furthermore, we investigate pairs of statistics on Andr\'e permutations and simsun permutations that are equidistributed with  the pair $(\asc, \last)$ on Jacobi permutations, where $\asc$ denotes the number of ascents of permutations.  Finally, we obtain a closed-form formula for the trivariate exponential generating function of Jacobi permutations with respect to the number of ascents and the numbers of letters smaller and larger than the last letter.  

报告人简介：严慧芳，浙江师范大学5278论坛 教授，博士生导师，主要研究组合结构的计数以及组合统计量方面的问题，在《J. Combin. Theory Ser. A》、《Adv. In Appl. Math.》、《European J. Combin.》等杂志发表论文近60篇，先后主持国家自然科学基金4项。

报告题目: A new family of $q$-supercongruences from the $q$-Dixon sum

摘要: Employing the $q$-Dixon sum, the creative microscoping method developed by the first author and Zudilin, and the Chinese remainder theorem for polynomials, we establish a family of $q$-supercongruences modulo the square or cube of a cyclotomic polynomial. As a conclusion, we obtain the supercongruence: for any prime $p\equiv 11\pmod{12}$,

$$

\sum_{k=0}^{(2p-1)/3}\frac{(\frac{1}{2})_{k}^2(\frac{1}{3})_{k}}{k!^{2}(\frac{7}{6})_{k}}

\equiv \frac{3}{7}\frac{(\frac{3}{2})_{(2p-1)/3}(\frac{7}{12})_{(2p-1)/3}}{(\frac{5}{4})_{(2p-1)/3}(\frac{1}{3})_{(2p-1)/3}}

+\frac{4}{7}\frac{(\frac{3}{2})_{(p-1)/2}(\frac{7}{12})_{(p-1)/2}}{(\frac{5}{4})_{(p-1)/2}(\frac{1}{3})_{(p-1)/2}}\pmod{p^3},

$$

where $(a)_n=a(a+1)\cdots(a+n-1)$ is the Pochhammer symbol. This extends a recent result modulo $p^2$ of Mao and Pan, which was derived

from the Dixon sum.

报告人简介：郭军伟教授，本科毕业于南开大学数学系，后师从中国科学院院士陈永川教授从事代数组合与g-级数理论研究，并于2004年获理学博士学位。随后赴法国里昂第一大学跟随曾江教授从事为期一年半的博士后研究，并在维也纳薛定谔国际数学物理研究所短期访问。2006年作为引进副教授在华东师范大学数学系任教，2011年破格升为教授、2012年任博士生导师。目前是杭州师范大学教授，博士生导师。郭军伟教授的研究领域主要涉及计数组合学、g-级数、同余式等三个方面，目前在SCI期刊上共发表论文170 多篇。其中一篇发表在《Advances in Mathematics》上。郭军伟教授先后主持国家自然科学青年基金一项、面上基金三项；江苏省自然科学基金面上项目一项；上海市科委青年科技启明星计划一项，并获得2026年国际基础科学大会前沿科学奖（数学）。

报告题目: On the anti-Ramsey problem for matchings

摘要:  An edge-colored graph is called rainbow if all its edges receive distinct colors. Given a graph $G$ and a subgraph $H\subseteq G$. The anti-Ramsey number of $H$ in $G$ is defined to be the maximum $k$ such that there is a $k$-edge-coloring of $G$ without any rainbow copy of $H$. The anti-Ramsey problem for graphs was introduced  Erd\H{o}s {\it et al.} in 1970s and developed rapidly during recent decades. In this talk, we will give an overview on the anti-Ramsey problem for matchings.

报告人简介：金泽民，浙江师范大学5278论坛 教授，博士生导师，研究方向图论和组合优化，主要研究图的结构、极值图论方面的问题，尤其在图的anti-Ramsey数的研究方面取得一系列的成果，发表论文60余篇，主持国家自然科学基金项目3项，主持浙江省自然科学基金2项。

报告题目：Web permutations, Seidel triangle and normalized $\gamma$-coefficients

摘要：The web permutations were introduced by Hwang, Jang and Oh to interpret the entries of the transition matrix between the Specht and $\mathrm{SL}_2$-web bases of the irreducible $\S_{2n}$-representation indexed by $(n,n)$. They conjectured that certain classes of web permutations are enumerated by the Seidel triangle. Using generating functions, Xu and Zeng showed that enumerating web permutations by the number of drops, fixed points and cycles gives rise to the normalized $\gamma$-coefficients of the $(\alpha,t)$-Eulerian polynomials. They posed the problems to prove their result combinatorially and to find an interpretation of the normalized $\gamma$-coefficients in terms of cycle-up-down permutations. In this work, we prove the enumerative conjecture of Hwang-Jang-Oh and answer the two open problems proposed by Xu and Zeng. This talk is based on joint work with Yao Dong and Qiongqiong Pan.

报告人简介：林志聪，山东大学数学与交叉科学研究中心教授，国家青年高层次人才。主要从事计数组合学的研究，在J. Combin. Theory Ser. A、Combinatorica等权威期刊发表SCI学术论文40余篇。任中国数学会组合数学与图论专业委员会委员、中国数学会计算机数学专业委员会委员和中国运筹学会图论组合分会青年理事。

报告地点：数学楼301

报告时间：2026年9月5日上午8:00-12:00