Speaker：Takao Komatsu (Zhejiang Sci-Tech University)

Time：2023-4-28, 10:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

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.