The diagonal polynomials of dimension four (Q1775741)

Let \(s({\mathbf x})= x_1+\cdots+ x_n\) for \(x_1,\dots, x_n\in\mathbb{N}\) and fixed \(n\in\mathbb{N}\). A bijective polynomial function (PF) from \(\mathbb{N}^n\) to \(\mathbb{N}\) is called diagonal if \(f({\mathbf x})< f({\mathbf y})\) when \(s({\mathbf x})< s({\mathbf y})\). A set of representatives for the equivalence classes with respect to index permutation of diagonal PFs is known for \(n= 2,3\). Here the case \(n= 4\) is investigated leading to 6 representatives.