Real Morse polynomials of degrees 5 and 6
Abstract
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 $a_1,\ldots,a_{n-1}$, where $a_i$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.02305
- arXiv:
- arXiv:1911.02305
- Bibcode:
- 2019arXiv191102305K
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 10 pages, 16 figures