9 citations · 13 across the 5 of their papers we have counts for
6 papers
Solving the Cauchy problem for a three-dimensional difference equation in a parallelepiped
Marina S. Apanovich, Alexander P. Lyapin, Konstantin V. Shadrin
The aim of this article is further development of the theory of linear difference equations with constant coefficients. We present a new algorithm for calculating the solution to t…
Computing Rational Generating Function of a Solution to the Initial Value Problem of Two-dimensional Difference Equation with Constant Coefficients
Alexey A. Kytmanov, Alexander P. Lyapin, Timur M. Sadykov
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for comput…
Asymptotics of Taylor Coefficients of a Rational Function in Two Variables with Linear Singularities
Alexander Lyapin
In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coeffici…
Riordan's Arrays and Two-Dimensional Difference Equations
Alexander P. Lyapin
In this paper, the describing of rational Riordan's arrays from the combinatorial analysis is represented as solutions of a Cauchy problem for two-dimensional difference equations…
On the Rationality of Multidimentional Recusive Series
Evgeniy K. Leinartas, Alexander P. Lyapin
In this paper, we identify a class of solutions to multidimensional difference equation with rational generating function.
Generating functions for vector partition functions and a basic recurrence relation
Alexander P. Lyapin, Sreelatha Chandragiri
We define a generalized vector partition function and derive an identity for generating series of such functions associated with solutions of basic recurrence relation of combinato…