A Computer-Generated Theorem by Shalosh B. Ekhad Consider the poset L:= , [{}, {1}, {1, 2}, {}, {1, 4}, {1, 2, 4, 5}] Let P[n] be the poset obtained from joining n copies of L together, by identifying the last, 3, vertices of the previous link to the first, 3, vertices of the next link Let , F[n](x, y, z), be the weight-enumerator of of all P-partitions of P[n], with the weight q^(sum of entries) a b c times the product of , x y z where , a, b, c, are the last , 3, entries of the P-partition F[n](x, y, z), satisfies the following functional-recurrence equation: 2 q y F[n - 1](1, q y z, 1) F[n](x, y, z) = -------------------------------- 2 (q y - 1) (q y z - 1) (q x - 1) 2 q x F[n - 1](q x y, q z, 1) F[n - 1](q y, q z, 1) + -------------------------------- - ----------------------------- 2 (q z - 1) (q y - 1) (q x - 1) (q z - 1) (q x - 1) (q x y - 1) 3 2 3 q x y F[n - 1](1, q x y z, 1) - ------------------------------------- 2 3 (q x - 1) (q x y - 1) (q x y z - 1) Subject to the intial condition 18 4 5 2 13 3 3 2 12 3 3 11 2 3 F[1](x, y, z) = (q y z x - q y z x - q y z x - q y z x 10 3 2 8 2 3 10 2 2 7 2 2 8 2 2 - q z y x - q y z x + q y z x + q y z x + q y z x 6 2 5 2 / 3 5 2 + q x y z + q z y - 1) / ((q x y z - 1) (q x y z - 1) (q y z - 1) / 6 5 4 3 (q z - 1) (q x y z - 1) (q y z - 1) (q y z - 1) (q z - 1) (q - 1)) The pure generating function for all P-partitions is F[n](1, 1, 1) This took, 4.280, seconds of CPU time