学术报告

题      目： Frobenius problem associated with the number of solutions

报  告  人：TAKAO KOMATSU   教授  (邀请人：袁平之 )

                                    浙江理工大学

时      间：3月30日  16：00-17：00

地     点：数科院东楼401

报告人简介:

       TAKAO KOMATSU教授是浙江理工大学特聘教授。他在数论和组合方面的许多问题都有独到的见解，已发表论文210多篇。他是组合恒等式方面国际上著名专家。

摘      要：

       Consider the number d(n;a_1,\dots,a_k) of non-negative integer solutions (x_1,\dots,x_k) of the linear diophantine equation n=a_1 x_1+\dots+a_k x_k, where a_1,\dots,a_k are positive integers. For a non-negative integer p, let S_p be the set of all n's such that d(n;a_1,\dots,a_k)>p. Then the set N_0\S_p is finite if and only if gcd(a_1,\dots,a_k)=1. The largest element and the cardinality of N_0\S_p are called the p-Frobenius number and the p-genus (p-Sylvester number), respectively.  When p=0, the study on S=S_0 with the (0-)Frobenius number and the (0-)genus is known as the famous linear diophantine problem of Frobenius.  In this talk, these backgrounds, tools and recent results for p>0 are given.