报告人简介：
高志成博士目前是加拿大Carleton大学数理统计系终生教授。主要研究领域: 组合数学与图论、随机图论与随机地图理论，曲面地图计数与分布理论, 博彩业管理。他是目前国际上为数不多的在组合数学与拓扑图论领域内具有世界顶尖水平的数学家之一。他在低维拓扑领域内，尤其是曲面上嵌入图的计数和概率分布研究方面的0-1率方面的工作具有一流水准。是目前国际上这些领域内的著名学者。在国际著名数学期刊上发表高水平学术论文50余篇，高教授在组合数学，概率统计和博弈论的应用方面也是国际上知名专家。目前同时担任澳门特别行政区政府及博彩业咨询顾问，制定和参与经理培训项目；多次到美国，加拿大，法国，澳大利亚，巴西，日本，南韩，新加坡，香港，澳门，台湾 等地讲学。在SIAM Journal On Computing, Journal of Combinatorial Theory, Journal of Graph Theory，J. of Combin.Ser(B)等国际顶级专业刊物发表论文50余篇，任Annals of Combinatorics和International Gambling Studies编委。
报告内容简介：Let $\Gamma$ be a finite additive group. An $m$-composition over $\Gamma$ is an $m$-tuple $(g_1,g_2,\ldots,g_m)$ over $\Gamma$.It is called an $m$-composition of $g$ if $\sum_{j=1}^m g_j = g$. A composition $(g_j)$ over $S$ is called {\em locally restricted} if there is a positive integer $\sigma$such that any $\sigma$ consecutive parts of $(g_j)$ satisfy certain conditions. Locally restricted compositions over $\Gamma$ are associated with walks in a de Bruijin graph.Under certain aperiodic conditions, we will show that the asymptotic number of $m$-compositions of $\gamma$ is independent of $\gamma$.We also show that the distribution of the number of occurrences of a set of subwords in such $m$-compositions is asymptotically normal with mean and variance proportional to $m$. The proofs use the transfer matrix, Kronecker product of matrices, and Perron-Frobenius theorem, and tools from analytic combinatorics

主持人：任韩 教授
主办单位：数学科学学院 科技处