Zobrazeno 1 - 10
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pro vyhledávání: '"Kruchinin, Dmitry"'
Autor:
Shablya, Yuriy, Kruchinin, Dmitry
In this paper, we study the combinatorial set of RNA secondary structures of length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set, we construc
Externí odkaz:
http://arxiv.org/abs/2301.11890
In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating function some well-known and new identities for the Euler number of th
Externí odkaz:
http://arxiv.org/abs/1802.09003
Akademický článek
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Autor:
Kruchinin, Dmitry1 (AUTHOR), Kruchinin, Vladimir1 (AUTHOR), Shablya, Yuriy1 (AUTHOR) syv@fb.tusur.ru
Publikováno v:
Mathematics (2227-7390). Jul2023, Vol. 11 Issue 13, p2859. 15p.
Autor:
Banderier, Cyril, Krattenthaler, Christian, Krinik, Alan, Kruchinin, Dmitry, Kruchinin, Vladimir, Nguyen, David Tuan, Wallner, Michael
Publikováno v:
in: Lattice Path Combinatorics and Applications, G. E. Andrews, C. Krattenthaler and A. Krinik (eds.), Developments in Mathematics, Springer-Verlag, Cham, 2019, pp. 78-11
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude $j$ and ending at a given altitude $k$, with additional constraints such as, for example, to never attain alt
Externí odkaz:
http://arxiv.org/abs/1609.06473
Autor:
Kruchinin, Dmitry, Kruchinin, Vladimir
Using the notion of the composita, we obtain a method of solving iterative functional equations of the form $A^{2^n}(x)=F(x)$, where $F(x)=\sum_{n>0} f(n)x^n$, $f(1)\neq 0$. We prove that if $F(x)=\sum_{n>0} f(n)x^n$ has integer coefficients, then th
Externí odkaz:
http://arxiv.org/abs/1302.1986
Autor:
Kruchinin, Dmitry
In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite numbers. Using the result of paper we get the known properties of the Bel
Externí odkaz:
http://arxiv.org/abs/1211.2100
Autor:
Kruchinin, Vladimir, Kruchinin, Dmitry
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials, Bernoulli
Externí odkaz:
http://arxiv.org/abs/1211.0099
Autor:
Kruchinin, Vladimir, Kruchinin, Dmitry
Publikováno v:
Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.3
We present techniques for obtaining a generating function for the central coefficients of a triangle $T(n,k)$, which is given by the expression $[xH(x)]^k=\sum_{n\geqslant k} T(n,k)x^n$, $H(0)\neq 0$. We also prove certain theorems for solving direct
Externí odkaz:
http://arxiv.org/abs/1206.0877
Autor:
Kruchinin, Dmitry
In this paper we obtained an original integer sequence based on the properties of the multinomial coefficient. We investigated a property of the sequence that shows connection with a primality testing. For any prime n the n-th term in the sequence is
Externí odkaz:
http://arxiv.org/abs/1204.6554