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, 2, vertices of the previous link to the first, 2, vertices of the next link Let , F[n](x, y), be the weight-enumerator of of all P-partitions of P[n], with the weight q^(sum of entries) a b times the product of , x y where , a, b, are the last , 2, entries of the P-partition F[n](x, y), satisfies the following functional-recurrence equation: 2 q x F[n - 1](1, q x y) F[n - 1](q x, q y) F[n](x, y) = - ----------------------- + ------------------- 2 (q y - 1) (q x - 1) (q x y - 1) (q x - 1) Subject to the intial condition 4 2 q y x - 1 F[1](x, y) = ----------------------------------------------------------- 2 3 4 2 (q y - 1) (q y - 1) (q y x - 1) (q x y - 1) (q x y - 1) The pure generating function for all P-partitions is F[n](1, 1) This took, 0.384, seconds of CPU time