报告题目：Enumeration and congruences of higher dimensional king walks

报告人：刘纪彩副教授，温州大学

报告时间：2024年4月15日（周一）14:30-16:30

报告地点：腾讯会议ID：564 215 693

报告摘要：The lattice walks in the plane starting at the origin ${\bf 0}$ with steps in $\{-1,0,1\}^{2}\setminus \{{\bf 0}\}$ are called king walks. We investigate enumeration and congruences for higher dimensional king walks confined to certain regions. Specifically, we establish an explicit formula for the number of $(r+s)$-dimensional king walks of length $n$ ending at $(a_1,\cdots,a_r,b_1,\cdots,b_s)$ which never dip below $x_i=0$ for $i=1,\cdots,r$. We also derive some congruences for the number of $(r+s)$-dimensional king walks of length $p$ (an odd prime). This is a joint work with Yeong-Nan Yeh.

报告人简介：刘纪彩，温州大学副教授，硕士生导师，主要从事组合数学与数论研究，迄今为止在Advances in Applied Mathematics、Journal of Number Theory、Proc. Amer. Math. Soc.等国际期刊上发表学术论文50余篇。作为项目负责人主持国家自然科学基金项目3项等，有关科研成果获山东省自然科学奖二等奖1项。