Enumeration of Unlabeled P-Series by Using the Poset Matrix

A. We give an exact enumeration of the unlabeled P -series, a subclass of the frequently studied series-parallel posets.In this enumeration method, we determine the number of unlabeled P -series according to the number of direct terms (connected components) of the posets.Here, we use the results regarding the matrix recognition of P -series by using the poset matrix.We also give an algorithm to determine the values of the parameters involved in the enumeration formula and to compute the number of unlabeled P -series with a certain number of elements.We show that the enumeration algorithm runs in polynomial time.We include the numerical results for the numbers of unlabeled P -series up to 76 elements.