Max A. Alekseyev

activity

20162026

most citedOn p-adic approximation of sums of binomial coefficients

1 citations · 1 across the 8 of their papers we have counts for

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Showing 2026Show all

7 papers · 1 filter

math.DS2026

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…

math.NT2026

Congruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution Sets

Max A. Alekseyev, Dmitry I. Khomovsky

Let $A$ and $B$ be polynomials with integer coefficients. We study nonzero integer solutions of $y ∣ A (x), x ∣ B (y),$ using quotient transformations that may change the…

math.RA2026

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…

math.RA2026

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…

math.RA2026

Constructive recurrences for determinants and permanents of banded Toeplitz matrices

Max A. Alekseyev, Dmitry I. Khomovsky

For fixed nonnegative integers $m_{1}, m_{2}$ , let $A_{n} = (a_{j - i})_{i, j = 1}^{n}$ be the leading $n \times n$ section of a Toeplitz matrix with lower and upper semibandwidths $m_{1}$ and $m_{2}$ .…

math.CO2026

Möbius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications

Max A. Alekseyev

A coefficient duality first encountered for formal Bernoulli series is shown to be equivalent to a general Möbius covariance law for formal power series. We obtain a structural cha…

math.NT2026

Computing bounded solutions to linear Diophantine equations with the sum of divisors

Max A. Alekseyev

We propose an efficient computational method for finding all solutions $n \leq U$ to the Diophantine equation $aσ (n) = bn + c$ , where $a, b, c$ are fixed integer coefficients, $U$ is a gi…