Speaker: Dr.Min Sha(University of New South Wales)
Title: Functional graphs generated by plane curves and their twists
Time: Wed, Nov.13 2019,PM:15:00-16:00
Location: Room 4131, Building No.4, Wushan Campus
Abstract:
Given a plane curve defined by Y^2 = f(X) over a finite field F_q of odd characteristic and a non-square element \lambda in F_q, we define a functional graph by choosing the elements in F_q as vertices and drawing an edge from x to y if and only if (x,y) is either a point on the curve Y^2 = f(X) or a point on the curve \lambda*Y^2 = f(X). We show that if f is a permutation polynomial over F_q, then every connected component of the graph has a Hamiltonian cycle. Moreover, these Hamiltonian cycles can be used to construct balancing binary sequences. By making computations for permutation polynomials f of low degree, it turns out that almost all these graphs are strongly connected, and there are many Hamiltonian cycles in such a graph if it is connected.