Let \((\Gamma,\Lambda)\) be a quiver (\(\Gamma\) a graph with possibly multiple edges, \(\Lambda\) its orientation). Assume it is finite and has no oriented cycles. The paper concerns the Bernstein-Gelfand-Ponomarev reflection functors on the category \(\text{f.d.}k(\Gamma,\Lambda)\) of finite dimensional representations of \((\Gamma,\Lambda)\) over a fixed field \(k\). Given a sink \(x\) in \((\Gamma,\Lambda)\), that is, a vertex which is not a starting point of any arrow, there is a reflection functor \(F_x^+\colon\text{f.d.}k(\Gamma,\Lambda)\to\text{f.d.}k(\Gamma,\sigma_x\Lambda)\), where \(\sigma_x\Lambda\) is the orientation obtained from \(\Lambda\) by reversing the arrows containing the vertex \(x\). It is known that the reflection functors play a fundamental role in the theory of representations of quivers, see \textit{I. N. Bernstein, I. M. Gel'fand} and \textit{V. A. Ponomarev} [Usp. Mat. Nauk 28, No. 2(170), 19-33 (1973; Zbl 0269.08001)]. A sequence \(S=(x_1,\dots,x_s)\) of vertices of \((\Gamma,\Lambda)\) is called (+)-admissible if \(x_1\) is a sink in \((\Gamma,\Lambda)\) and \(x_i\) is a sink in \((\Gamma,\sigma_{x_{i-1}}\cdots\sigma_{x_{1}}\Lambda)\) for \(i=2,\dots,s\). Let \(F_S=F^+_{x_s}\cdots F^+_{x_1}\). A representation \(M\) of \((\Gamma,\Lambda)\) is called preprojective if \(F_S(M)=0\) for some \(S\). Two admissible sequences are said to be equivalent if one can be obtained from the other by a sequence of transpositions of two consecutive elements which are not connected by an edge in \(\Gamma\). It is proved that for each indecomposable preprojective \(M\) there is unique, up to equivalence, shortest (+)-admissible sequence \(S\) such that \(F_S(M)=0\). Denote the sequence by \(S_M\). The isomorphism class of \(M\) is determined by \(S_M\). There is a natural partial order on the set of equivalence classes of (+)-admissible sequences: \(S\preceq T\) provided \(T\) is a prolongation of \(S\) on the right. The properties of the poset formed by all sequences \(S_M\) are discussed in the paper. Given an indecomposable preprojective representation \(M\) let \(S(\to M)\) by the additive hull of the set of all predecessors \(X\) of \(M\) in the preprojective component such that every path from \(X\) to \(M\) is sectional, see \textit{C. M. Ringel} [Tame algebras and integral quadratic forms, Lect. Notes Math. 1099 (1984; Zbl 0546.16013)]. Another result of the paper asserts that \(S(\to M)\) is a slice if and only if every vertex of \(\Gamma\) occurs in the sequence \(S_M\).