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We construct a complete set of reflection functors for the representations of posets and prove that they really have the usual properties. In particular, when the poset is of finite representation type, all of its indecomposable representations can be obtained from some "trivial" ones via relations. To define such reflection functors, a wider class of matrix problem is introduced, called "representations of bisected posets".
The combinatorial interest in posets is largely due to two unoriented graphs associated with a given poset: the comparability graph (which we shall not consider here) and the covering graph.