General mathematics seminar

July 19, 2018. Zhi-Wei Sun (Nanjing University). Determinants, Permutations and Additive Combinatorics.

In this talk we will introduce some new problems and related progress on determinants involving Legendre symbols, circular permutations and additive combinatorics. For example, we conjecture that for any finite subset A of an additive cyclic group G with |A|=n>3 there is a circular permutation a1, …, an of the elements of A such that all the n sums

a1+a2+a3, a2+a3+a4, …, an-2+an-1+an, an-1+an+a1, an+a1+a2

are pairwise distinct. The speaker has proved this when G is the infinite cyclic group Z.

List of talks at previous sessions of the seminar.