3 citations · 4 across the 8 of their papers we have counts for
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Multivariable Congruence Jumping: Periodic States, Integral Realizations, and Descent
Max A. Alekseyev, Dmitry I. Khomovsky
Congruence jumping replaces coordinates by integer quotients and updates polynomial divisibility relations. We extend this procedure to several variables and retain integer coeffic…
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 .…