In this paper we find an exact formula for the number of partitions of an element $z$ into $m$ parts over a finite field, i.e. we find the number of nonzero solutions of the equation $x_1+x_2+\cdots +x_m=z$ over a finite field when the order of terms does not matter. This is equivalent to counting the number of $m$-multi-subsets whose sum is $z$. When the order of the terms in a solution does matter, such a solution is called a composition of $z$. The number of compositions is useful in the study of zeta functions of toric hypersurfaces over finite fields. We also give an application in the study of polynomials of prescribed ranges over finite fields.
@article{10_37236_2678,
author = {Amela Muratovic-Ribic and Qiang Wang},
title = {Partitions and compositions over finite fields},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2678},
zbl = {1283.11145},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2678/}
}
TY - JOUR
AU - Amela Muratovic-Ribic
AU - Qiang Wang
TI - Partitions and compositions over finite fields
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2678/
DO - 10.37236/2678
ID - 10_37236_2678
ER -
%0 Journal Article
%A Amela Muratovic-Ribic
%A Qiang Wang
%T Partitions and compositions over finite fields
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2678/
%R 10.37236/2678
%F 10_37236_2678
Amela Muratovic-Ribic; Qiang Wang. Partitions and compositions over finite fields. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2678
