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We present an algorithm for finding a system of recurrence relations for the number of permutations of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts permutations by their length and the indices of the… (More)

abstract Several authors have examined connections among restricted permutations and different combina-torial structures. In this paper we establish a bijection between the set of permutations π which avoid 1322 and the set of odd-dissection convex polygons, where a permutation avoids ab2c if there are no i < j < k − 1 such that π i π j π k is… (More)

Inspired by the results of Stanley and Widom concerning the limiting distribution of the lengths of longest alternating subsequences in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequence for pattern-restricted permutations, we find the limiting distribution of the longest… (More)

We present an algorithm for finding a system of recurrence relations for the number of k-ary words of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts k-ary words by their length and the indices of the… (More)

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