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In this paper we study finite Eulerian posets which are binomial, Sheffer ortriangular. These important classes of posets are related to the theory ofgenerating functions and to geometry. The results of this paper are organizedas follows:  We completely determine the structure of Eulerian binomial posets and, as aconclusion, we are able to classify factorial functions of Eulerian binomialposets;  We give an almost complete classification of factorial functions of EulerianSheffer posets by dividing the original question into several cases;  In most cases above, we completely determine the structure of EulerianSheffer posets, a result stronger than just classifying factorial functions ofthese Eulerian Sheffer posets.  We also study Eulerian triangular posets. This paper answers questions askedby R. Ehrenborg and M. Readdy. This research is also motivated by the work ofR. Stanley about recognizing the boolean lattice by looking at smallerintervals.

Finite Eulerian posets which are binomial, Sheffer or triangular