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Fundamentalnaya i Prikladnaya Matematika, 2021, Volume 23, Issue 4, Pages 99–112
(Mi fpm1912)
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Real Morse polynomials of degree $5$ and $6$
Yu. Yu. Kochetkov National Research University Higher School of Economics, Moscow, Russia
Abstract:
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.
Citation:
Yu. Yu. Kochetkov, “Real Morse polynomials of degree $5$ and $6$”, Fundam. Prikl. Mat., 23:4 (2021), 99–112; J. Math. Sci., 269:4 (2023), 512–522
Linking options:
https://www.mathnet.ru/eng/fpm1912 https://www.mathnet.ru/eng/fpm/v23/i4/p99
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Abstract page: | 85 | Full-text PDF : | 45 | References: | 13 |
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