Andrey Ryabichev

collaborators

4 papers

math.CO2024

Chebyshev polynomials, their remarkable properties and connection with Catalan numbers

Andrey Ryabichev, Konstantin Shcherbakov

The main result of the article says that the formal power series equal to the ratio of two neighboring Chebyshev polynomials, after some renormalization, approximates the generatin…

math.CA2024

Roots of polynomials and tangents of circles

Andrey Ryabichev, Konstantin Shcherbakov

Given a real cubic function $f (x)$ with three roots, take an equilateral triangle $A B C$ , the projections of which vertices are the roots of $f (x)$ . There is a folklore fact that th…

math.GT2024

Short proof of the Kneser-Edmonds theorem on the degree of a map between closed surfaces

Andrey Ryabichev

Suppose for closed surfaces $M, N$ there exists a continuous map $f : M \to N$ of geometric degree $d > 0$ . Then $χ (M) \leq d \cdot χ (N)$ . This inequality was first proved by Kneser in case…

math.HO2023

Immersions of manifolds

Andrey Ryabichev

This text is based on my talk at the popular science conference ``Dark geometry fest'' which was related to geometric methods and their applications, July 17, 2022. We will move to…