报告题目：The Ring of Isobaric Polynomials
报告人：Dr. Trueman MacHenry , York University
摘要：An isobaric polynomial is a symmetric polynomial written on the ESP (Elementary Symmetric Polynomials). We consider two especially interesting linearly recursive sequences in this ring, the Generalized Fibonacci Polynomials (GFP) and the Generalized Lucas Polynomials(GLP). We equip this ring with a convolution product, which is a version of the Dirichlet Product in Arithmetic Function Theory. There are two especially interesting groups: one is the Group of Multiplicative Arithmetic functions, and the other is the Group of Additive Arithmetic Functions. These two groups have faithful representation in the Isobaric Ring, namely, using, respectively, the GFP’s and the GLP’s.