1 citations · 1 across the 8 of their papers we have counts for
12 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 .…
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…
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 to the Diophantine equation , where are fixed integer coefficients, is a gi…
Classifying integral Grothendieck rings up to rank 5 and beyond
Max A. Alekseyev, Winfried Bruns, Jingcheng Dong +1
In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its fo…
Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series
Max A. Alekseyev, Rafael Gonzalez, Keryn Loor +2
Faulhaber's formula expresses the sum of the first positive integers, each raised to an integer power , as a polynomial in of degree . Ramanujan expressed thi…
On the -adic valuations of values of Legendre polynomials
Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1
We prove an explicit formula for the -adic valuation of the Legendre polynomials evaluated at a prime , and generalize an old conjecture of the third author. We also…
Three Cousins of Recaman's Sequence
Max A. Alekseyev, Joseph Samuel Myers, Richard Schroeppel +3
Although 10^230 terms of Recaman's sequence have been computed, it remains a mystery. Here three distant cousins of that sequence are described, one of which is also mysterious. (i…
On p-adic approximation of sums of binomial coefficients
Rustem R. Aidagulov, Max A. Alekseyev
We propose higher-order generalizations of Jacobsthal's -adic approximation for binomial coefficients. Our results imply explicit formulae for linear combinations of binomial co…