Title：LUCAS SEQUENCES AND PERMUTATION BEHAVIOR OF POLYNOMIALS OVER FINITE FIELDS

Speaker：Qiang Wang, Department of Mathematics, Carleton University

Date：2010-1-20(Wednesday), 10:00am

Venue：Conference Hall 322，Science Building

Abstract：A polynomial f over a finite field Fq is called a permutation polynomial of Fq if the mapping f permutes the elements of Fq. Permutation polynomials were first investigated by Hermite, and since then, many studies concerning them have been devoted. In the last 20 years there has been a revival in the interest for permutation polynomials, in part due to their applications in combinatorics and cryptography.

The Lucas sequence is a second order linear recurring sequence which has the same recurrence relation as Fibonacci sequence but initial values are different. It is one of most elementary combinatorial objects and it has several interesting applications. In this talk, we introduce so-called generalized Lucas sequences of any order and show that generalized Lucas sequences over finite prime fields are closely related to permutation behavior of some classes of polynomials and their compositional inverses over some extension fields.