April 30, 2024
Join us as Emily Shambaugh '24 presents "Factorization Patterns of Polynomials and Partitions". Lunch provided and everyone is welcome to attend.
Abstract: A partition of a natural number n is a non-increasing sequence of natural numbers that sum to n. For example, the partitions of four are: 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. In this talk, we explain how certain types of partitions can be used to describe the ways a polynomial of degree n may factor. We provide a recursive formula for the number of these partitions and generalize these ideas to the case of two polynomials whose degrees sum to n.