Bijections for refined restricted permutations
نویسندگان
چکیده
منابع مشابه
Bijections for refined restricted permutations
We present a bijection between 321and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson et al. (Ann. Combin. 6 (2003) 427), and Elizalde (Proc. FPSAC 2003). We also show that our bijection preserves additional statistics, which extends the
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We present a bijection between 321and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson, Saracino and Zeilberger [8], and the first author [3]. We also show that our bijection preserves additional statistics, which extends the previous results.
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Define Sk n(α) to be the set of permutations of {1, 2, . . . ,n} with exactly k fixed points which avoid the pattern α∈ Sm. Let sn(α) be the size of Sk n(α). We investigate S0 n(α) for all α∈ S3 as well as show that sn(132) = s k n(213) = s k n(321) and s k n(231) = s k n(312) for all 0 ≤ k ≤ n.
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In the present paper we study general properties of good sequences by means of a powerful and beautiful tool of combinatorics—the method of bijective proofs. A good sequence is a sequence of positive integers k = 1, 2, . . . such that the element k occurs before the last occurrence of k + 1. We construct two bijections between the set of good sequences of length n and the set of permutations of...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2004
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2003.10.009