A characterization of incomplete sequences in vector spaces

A sequence A of elements an additive group G is incomplete if there exists a group element that cannot be expressed as a sum of elements from A. The study of incomplete sequences is a popular topic in combinatorial number theory. However, the structure of incomplete sequences is still far from being understood, even in basic groups.The main goal of this paper is to give a characterization of incomplete sequences in the vector space , where d is a fixed integer and p is a large prime. As an application, we give a new proof for a recent result by Gao, Ruzsa and Thangadurai on Olsonʼs constant of and partially answer their conjecture concerning .