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Counting polynomials over finite fields with prescribed leading coefficients and linear factors

作者:时间:2021-12-28点击数:

报告地址链接:Join Zoom Meeting

https://carleton-ca.zoom.us/j/93751893273

Meeting ID: 937 5189 3273

报告时间:2022-01-08,上午9:30-10:30(周六)


报告题目:Counting polynomials over finite fields with prescribed leading coefficients and linear factors

报告人:Zhicheng Gao School of Mathematics and Statistics,Carleton University, Ottawa, Ontario, Canada


报告摘要:We count polynomials over finite fields with prescribed leading coefficients and a given number of linear factors. This is equivalent to counting codewords in Reed-Solomon codes which are at a certain distance from a received word. Generating functions defined on a group algebra are used to keep track of the equivalence classes of leading coefficients. The sieve formula of Li and Wan's is applied to simplify the generating functions in some special cases. The moments of the distance between a received word and random codewords in a Reed-Solomon code can also be obtained in general. Our results extend and improve some recent results by Li and Wan, and Zhou, Wang and Wang.

高志成教授早年就读于南京大学数学系,1984年被著名美籍华人数学家,菲尔奖获得者邱成桐教授作为优秀人才选拔出国深造,1989年获得美国加利福利亚大学博士学位。自1996年在加拿大Carleton大学数理统计系任教,2002年晋升为终生教授。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。目前是著名的南开大学组合数学中心陈省身讲席教授,澳门大学工商管理学院特聘教授,博彩研究所所长。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,中国大陆,香港,澳门,台湾 等地讲学。在国际著名数学期刊上发表高水平学术论文50余篇,任Annals of Combinatorics和International Gambling Studies编委。

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