Results 31 to 40 of about 616,883 (325)
On difference polynomials and hereditarily irreducible polynomials
Journal of Number Theory, 1980 AbstractA difference polynomial is one of the form P(x, y) = p(x) − q(y). Another proof is given of the fact that every difference polynomial has a connected zero set, and this theorem is applied to give an irreducibility criterion for difference polynomials. Some earlier problems about hereditarily irreducible polynomials (HIPs) are solved.
Rubel, L.A, Schinzel, A, Tverberg, H
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Difference equation of the colored Jones polynomial for torus knot
, 2004 We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a case of T_{2,2m+1}.
Andrews G. E. +2 more
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Difference dimension quasi-polynomials
Advances in Applied Mathematics, 2017 We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that such functions are quasi-polynomials, which can be represented as alternative sums of Ehrhart quasi-polynomials ...
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Characteristic Polynomial Patterns in Difference Sets of Matrices
, 2015 We show that for every subset $E$ of positive density in the set of integer square-matrices with zero traces, there exists an integer $k \geq 1$ such that the set of characteristic polynomials of matrices in $E-E$ contains the set of \emph{all ...
Björklund, Michael, Fish, Alexander
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Differential Galois Theory of Linear Difference Equations [PDF]
, 2008 We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations.
Hardouin, Charlotte, Singer, Michael F.
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Zeros of difference polynomials
Journal of Approximation Theory, 1992 Studies --- both analytic and numerical --- on polynomials have been of immense interest for long. Here the authors deal in detail with various questions relating to the zeros of difference polynomials. Particularly, defining the difference operator by \(\Delta f(x)=f(x+1)-f(x)\), the polynomial \(\Delta^ mx^ n\) of degree \((n-m)\) having \((n-m ...
Evans, Ronald J, Wavrik, John J
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Meromorphic functions that share a polynomial with their difference operators
Advances in Difference Equations, 2018 In this paper, we prove the following result: Let f be a nonconstant meromorphic function of finite order, p be a nonconstant polynomial, and c be a nonzero constant.
Bingmao Deng +3 more
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Positive Polynomials on Riesz Spaces
, 2016 We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that positive, additive mappings are linear.
Cruickshank, James +2 more
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A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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Difference equations on discrete polynomial hypergroups
Advances in Difference Equations, 2006 The classical theory of homogeneous and inhomogeneous linear difference equations with constant coefficients on the set of integers or nonnegative integers provides effective solution methods for a wide class of problems arising from different fields of ...
Orosz Ágota
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