Pattern avoidance in compositions and multiset permutations

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Abstract

We show that among the compositions of n into positive parts, the number g(n) that avoid a given pattern π of three letters is independent of π. We find the generating function of {g(n)}, and it shows that the sequence {g(n)} is not P-recursive. If S is a given multiset, we show that the number of permutations of S that avoid a pattern π of three letters is independent of π. Finally, we give a bijective proof of the fact that if M=1a1...kak is a given multiset then the number of permutations of M that avoid the pattern (123) is a symmetric function of the multiplicities a1,...,ak. The bijection uses the Greene-Kleitman symmetric chain decomposition of the Boolean lattice. © 2005 Elsevier Inc. All rights reserved.

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APA

Savage, C. D., & Wilf, H. S. (2006). Pattern avoidance in compositions and multiset permutations. Advances in Applied Mathematics, 36(2), 194–201. https://doi.org/10.1016/j.aam.2005.06.003

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