Author

Max A. Alekseyev

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Preprint Sep 2026

Symmetry reductions and recurrence degrees for banded Toeplitz determinants and permanents

This paper studies symmetry-induced reductions of scalar recurrence complexity for balanced banded Toeplitz determinants and permanents. Three mechanisms emerge: determinant state and spectral compression, exceptional permanent--determinant conversion, and symmetries of permanent state spaces. For symmetric determinant...

Max A. Alekseyev, D. I. Khomovsky · 0 citations

Preprint Sep 2026

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

Let $A$ and $B$ be polynomials with integer coefficients. We study nonzero integer solutions of $$y\mid A(x),\qquad x\mid B(y),$$ using quotient transformations that may change the polynomial pair. We call this process \emph{congruence jumping}. We establish a general reciprocal-polynomial rule governing such jumps, wi...

Max A. Alekseyev, D. I. Khomovsky · 0 citations

Preprint Sep 2026

Constructive recurrences for determinants and permanents of banded Toeplitz matrices

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 $m_2$. We give two constructive Laplace-expansion methods for scalar recurrences of $\det A_n$ and $\perm A_n$. The increasing-rows method elimina...

Max A. Alekseyev, D. I. Khomovsky · 2 citations · ⚡1