Created: Sept-Dec., 2003. This version: Dec. 1, 2003 This is SMCper, a Maple package to implement Doron Zeilberger's Symbolic Moment Calculus applied to patterns in permutations as it is described in his article Symbolic Moment Calculus: I. Foundations and Permutation-Patterns Written by Doron Zeilberger, zeilberg@math.rutgers.edu `` Please report bugs to zeilberg@math.rutgers.edu `` The most current version of this package and paper are available from http://www.math.rutgers.edu/~zeilberg/ For a list of the MAIN procedures type ezra();, for help with a specific procedure, type ezra(procedure_name); For a list of the supporting procedures type ezra1();, for help with a specific supporting procedure, type ezra1(procedure_name); Warning, the protected name Chi has been redefined and unprotected The exact (not asymptotic) expression for the, 3, -th moment of the Random Variable on S_n, #of occurences of the pattern [1, 2, 3], and its images is 4 3 2 n (n - 1) (n - 2) (1437 n + 5592 n - 11277 n - 33990 n + 34082) ------------------------------------------------------------------ 6350400 The exact (not asymptotic) expression for the, 3, -th moment of the Random Variable on S_n, #of occurences of the pattern [1, 3, 2], and its images is 4 3 2 n (n - 1) (n - 2) (129 n + 3705 n + 5355 n + 8655 n + 11356) --------------------------------------------------------------- 12700800 The whole thing took, 435.082, of CPU time