The number of solutions to linear Diophantine equations and multivariate splines
نویسندگان
چکیده
منابع مشابه
Multivariate Discrete Splines and Linear Diophantine Equations
In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a necessary and sufficient condition for the integer translates of a discrete box spline to be linearly ind...
متن کاملThe Number of Solutions of Diophantine Equations
0. Introduction. In two recent papers 4], 30], Erdd os, Stewart and the author showed that certain diophantine equations have many solutions. In this way they indicated how far certain results are capable for improvements at most. First we mention some relevant results from the literature on upper bounds for the numbers of solutions of diophantine equations and then we sketch how our method lea...
متن کاملSmall solutions of linear Diophantine equations
Let Ax = B be a system of m x n linear equations with integer coefficients. Assume the rows of A are linearly independent and denote by X (respectively Y) the maximum of the absolute values of the m x m minors of the matrix A (the augmented matrix (A, B)). If the system has a solution in nonnegative integers, it is proved that the system has a solution X = (xi) in nonnegative integers with xi <...
متن کاملSparse Solutions of Linear Diophantine Equations
We present structural results on solutions to the Diophantine system Ay = b, y ∈ Z ≥0 with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel’s Lemma, generating functions, and commutative algebra. These results have some interesting consequences in discrete optimization.
متن کاملOptical solutions for linear Diophantine equations
Determining whether a Diophantine equation has a solution or not is the most important challenge in solving this type of problems. In this paper a special computational device which uses light rays is proposed to answer this question, namely check the existence of nonnegative solutions for linear Diophantine equations. The way of representation for this device is similar to an directed graph, h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1988
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1988-0951619-x