Generating Ouroboros Polynomials and Ouroboros Matrices

Abstract: Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods, we demonstrate that a collection of second-order polynomials can be generated for any multivariable Ouroboros function of the form we have mentioned in previous works ([1] [2]). We then generalize this observation to higher-order polynomials using the properties of Ouroboros spaces and the results of some of our previously proven theorems. After discussing the generation of these polynomials, we conclude by constructing a matrix from them and provide a few comments on its structure and aesthetic, culminating in the derivation of an intuitive formula for the degree of the trace of the square cases of these matrices and the discussion of some future research prospects.