活动地点：

活动类型：学术报告

主讲人：Phill Schultz

活动时间：

活动内容：

1. 数 学 演 讲
Lecturer:  Professor Phill Schultz
School of Mathematics and Statistics,
University of Western Australia
Title: Integer Sequences Generated by Polynomials
Time：July 7 (周五) 10:30－11:30am, 2006;
Place：浙江大学数学中心202室
Abstract：An integral vector $\\ba=(a_1,a_2,\\dots,a_n)$  is called a \\textbf{polynomial sequence} if there is a polynomial $f(x)$ with integer coefficients such that $f(k)=a_k$ for $k=1,\\dots n$. I construct a rational $n\\times n$ matrix $A$ such that for all vectors $\\ba$ of length $n$, $\\ba$ is a polynomial sequence if and only if $A\\ba$ is an integral vector. From this result, I deduce the probability that a random integral vector is a polynomial sequence.
Extending this result to   infinite sequences leads to some interesting algebra:  new bases for the free abelian group of countable rank, and new subgroups and factor groups of the Baer--Specker group, the direct product of countably many copies of the integers.