# Download e-book for kindle: East side, West side. Lectures on combinatorial objects with by Wilf H.

By Wilf H.

This fabric is meant for a direction that may mix a research of combinatorial buildings with introductory recursive programming in Maple.

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Extra resources for East side, West side. Lectures on combinatorial objects with Maple

Sample text

Line 10: Here we successively concatenate the list out with k other lists, the ith one of which is the list of all partitions where n lives in class i, completing the construction. 65 Program RandSetPtns, on page 42, chooses a random partition of an n-set into k classes. line 7: To generate random numbers in the range (0, 1) we make the program rno. line 8: Now we choose such a random number, and if it is less than go east, else west. n−1 k−1 / n k we will line 10: To go east, we generate, recursively, a random set partition of an n − 1-set into k − 1 classes, and adjoin n as the singleton kth class.

So calculate the number p, and then choose a random is obviously p = n−1 k−1 real number ξ in the range (0, 1). If ξ < p then the output will be an east side permutation, and otherwise it will be a west side permutation. If the output is to be from the east side, then here’s what to do. Recursively, choose uar a permutation of n − 1 letters with k − 1 cycles, and then glue onto it a new cycle that contains only the letter n. Finished. Otherwise, if you want a west side permutation, then recursively choose uar a permutation of n − 1 letters with 33 k cycles.

A part ≤ k). If we subtract k from the left side, and delete one of the k’s from the right, we will be looking at some partition of n − k whose largest part is k. , we will have a west side partition of n. That means that altogether, there are p(n − k, k) partitions that are stacked up on the west side. It follows that p(n, k) = p(n − 1, k − 1) + p(n − k, k), since every partition of n landed on one side of town or the other. 1) with the initial values p(n, k) = 0 if n ≤ 0 or k ≤ 0 or k > n, and p(1, 1) = 1.