Number of solutions in a box of a linear equation in an Abelian group

Maciej Zakarczemny. "Number of solutions in a box of a linear equation in an Abelian group." Colloquium Mathematicae 143.1 (2016): 17-22. <http://eudml.org/doc/283935>.

@article{MaciejZakarczemny2016,
abstract = {For every finite Abelian group Γ and for all $g,a₁,..., a_\{k\} ∈ Γ$, if there exists a solution of the equation $∑_\{i=1\}^\{k\} a_\{i\}x_\{i\} = g$ in non-negative integers $x_\{i\} ≤ b_\{i\}$, where $b_\{i\}$ are positive integers, then the number of such solutions is estimated from below in the best possible way.},
author = {Maciej Zakarczemny},
journal = {Colloquium Mathematicae},
keywords = {abelian group; linear homogeneous equation; linear inhomogeneous equation; box; number of solutions},
language = {eng},
number = {1},
pages = {17-22},
title = {Number of solutions in a box of a linear equation in an Abelian group},
url = {http://eudml.org/doc/283935},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Maciej Zakarczemny
TI - Number of solutions in a box of a linear equation in an Abelian group
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 1
SP - 17
EP - 22
AB - For every finite Abelian group Γ and for all $g,a₁,..., a_{k} ∈ Γ$, if there exists a solution of the equation $∑_{i=1}^{k} a_{i}x_{i} = g$ in non-negative integers $x_{i} ≤ b_{i}$, where $b_{i}$ are positive integers, then the number of such solutions is estimated from below in the best possible way.
LA - eng
KW - abelian group; linear homogeneous equation; linear inhomogeneous equation; box; number of solutions
UR - http://eudml.org/doc/283935
ER -