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Working paper

Real Morse polynomials of degrees 5 and 6

arxiv.org. math. Cornell University, 2019. No. 1911.02305.
A real polynomial p of degree n is called a Morse polynomial if its derivative has n−1 pairwise differentreal roots and values of p in these roots (critical values) are also pairwise different. The plot of such polynomial is called a "snake". By enumerating critical points and critical values in the increasing order we construct a permutation a1,…,an−1, where ai is the number of polynomial's value in i-th critical point. This permutation is called the \emph{passport} of the snake (polynomial). In this work for Morse polynomials of degrees 5 and 6 we describe the partition of the coefficient space into domains of constant passport.