Geodesic
Real Morse polynomials of degree $5$ and $6$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 99-112.

Voir la notice de l'article provenant de la source Math-Net.Ru

A real polynomial $p$ of degree $n$ is called a Morse polynomial if its derivative has $n-1$ pairwise distinct real roots and values of $p$ at these roots (critical values) are also pairwise distinct. The plot of such a polynomial is called a “snake.” By enumerating critical points and critical values in increasing order, we construct a permutation $a_1,\dots,a_{n-1}$, where $a_i$ is the number of the polynomial's value at the $i$th critical point. This permutation is called the passport of the snake (polynomial). In this work, for Morse polynomials of degree $5$ and $6$, we describe the partition of the coefficient space into domains of constant passport. 
@article{FPM_2021_23_4_a6,
     author = {Yu. Yu. Kochetkov},
     title = {Real {Morse} polynomials of degree $5$ and $6$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {99--112},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a6/}
}
TY  - JOUR
AU  - Yu. Yu. Kochetkov
TI  - Real Morse polynomials of degree $5$ and $6$
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2021
SP  - 99
EP  - 112
VL  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a6/
LA  - ru
ID  - FPM_2021_23_4_a6
ER  - 
%0 Journal Article
%A Yu. Yu. Kochetkov
%T Real Morse polynomials of degree $5$ and $6$
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2021
%P 99-112
%V 23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a6/
%G ru
%F FPM_2021_23_4_a6
Yu. Yu. Kochetkov. Real Morse polynomials of degree $5$ and $6$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 99-112. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a6/

[1] Arnold V. I., “Ischislenie zmei i kombinatorika chisel Bernulli, Eilera i Springera grupp Kokstera”, UMN, 47:1 (1992), 3–45 | MR | Zbl

[2] Itenberg I., Zvonkine D., Hurwitz numbers for real polynomials, 2016, arXiv: 1609.05219 | MR | Zbl