A Computer-Generated Theorem by Shalosh B. Ekhad



               Consider the poset L:= , [{}, {1}, {1}, {1, 2, 3}]

             Let P[n] be  the poset obtained from joining n copies

              of L together, by identifying the last, 1, vertices

        of the previous link to the first, 1, vertices of the next link

                  Let , F[n](x),  be the weight-enumerator of

        of all P-partitions of P[n], with the weight q^(sum of entries)

                                                    a
                           times  the product of , x

                     where , a, are the last , 1, entries

                              of the P-partition



                       F[n](x), satisfies the following

                         functional-recurrence equation:

                                   4  2                3
                                 (q  x  - 1) F[n - 1](q  x)
                  F[n](x) = - --------------------------------
                                          2       2   3
                              (q x - 1) (q  x - 1)  (q  x - 1)



                        Subject to the intial condition

                                         4  2
                                        q  x  - 1
             F[1](x) = -------------------------------------------
                                   2       2   3          4
                       (q x - 1) (q  x - 1)  (q  x - 1) (q  x - 1)



              The pure generating function for all P-partitions is

                                    F[n](1)

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