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math.DS2024
Mathematical and physical billiard in pyramids
Yury Kochetkov, Lev Pyatko
In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be…
math.CO2024
Combinatorics of generic 5-degree polynomials
Yury Kochetkov
We consider the space of generic complex 5-degree polynomials. Critical values of such polynomial, i.e. four points in the complex plane, either are vertices of a convex quadra…
math.NT2024
On cubic polynomials with the cyclic Galois group
Yury Kochetkov
A cubic Galois polynomial is a cubic polynomial with rational coefficients that defines a cubic Galois field. Its discriminant is a full square and its roots (enumera…