3 citations · 4 across the 8 of their papers we have counts for
11 papers
Reciprocal Dynamics in Polynomial Congruence Jumping: Integral Orbits and Valuation Cones
Max A. Alekseyev, Dmitry I. Khomovsky
Alternating reciprocal transformations of polynomial divisibility systems couple an orbit of integer points to a rational dynamical system on polynomial coefficients. For fixed pos…
Congruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution Sets
Max A. Alekseyev, Dmitry I. Khomovsky
Let and be polynomials with integer coefficients. We study nonzero integer solutions of using quotient transformations that may change the…
Toeplitz multiplication and graded factorization of determinant recurrences
Max A. Alekseyev, Dmitry I. Khomovsky
We study how determinant recurrences of banded Toeplitz matrices behave when their Laurent symbols are multiplied. Two classical structures underlie the problem. Clean banded Toepl…
Symmetry reductions and recurrence degrees for banded Toeplitz determinants and permanents
Max A. Alekseyev, Dmitry I. Khomovsky
This paper studies symmetry-induced reductions of scalar recurrence complexity for balanced banded Toeplitz determinants and permanents. Three mechanisms emerge: determinant state…
Constructive recurrences for determinants and permanents of banded Toeplitz matrices
Max A. Alekseyev, Dmitry I. Khomovsky
For fixed nonnegative integers , let be the leading section of a Toeplitz matrix with lower and upper semibandwidths and .…
On natural densities of sets of some type integers
Dmitry I. Khomovsky
Let and be integers. Let be the number of integers between and such th…
On using symmetric polynomials for constructing root finding methods
Dmitry I. Khomovsky
We propose an approach to constructing iterative methods for finding polynomial roots simultaneously. One feature of this approach is using the fundamental theorem of symmetric pol…
A geometric approach to integer factorization
Dmitry I. Khomovsky
We give a geometric approach to integer factorization. This approach is based on special approximations of segments of the curve that is represented by , where is the in…
Efficient computation of terms of linear recurrence sequences of any order
Dmitry I. Khomovsky
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indi…
A method for obtaining Fibonacci identities
Dmitry I. Khomovsky
For the Lucas sequence we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrenc…
On the relationship between the number of solutions of congruence systems and the resultant of two polynomials
Dmitry I. Khomovsky
Let be an odd prime and , be polynomials with integer coefficients. If the system of congruences has solutions, then $R…