Asymptotic Properties of Compositions over Finite Groups
讲座名称：
Asymptotic Properties of Compositions over Finite Groups
讲座时间：
2019-03-06
讲座人：
高志成
形式：
校区：
兴庆校区
实践学分：
讲座内容：
报告题目：Asymptotic Properties of Compositions over Finite Groups
报告时间：2019年3月6号(星期三)16：10-17：10
报告地点：北五楼301(右)
报告人：高志成教授，加拿大Carleton大学
报告摘要：
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.
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