Some permutations on Dyck words
نویسندگان
چکیده
منابع مشابه
Dyck paths and restricted permutations
This paper is devoted to characterize permutations with forbidden patterns by using canonical reduced decompositions, which leads to bijections between Dyck paths and Sn(321) and Sn(231), respectively. We also discuss permutations in Sn avoiding two patterns, one of length 3 and the other of length k. These permutations produce a kind of discrete continuity between the Motzkin and the Catalan n...
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A bicoloured Dyck path is a Dyck path in which each up-step is assigned one of two colours, say, red and green. We say that a permutation π is σ-segmented if every occurrence o of σ in π is a segment-occurrence (i.e., o is a contiguous subword in π). We show combinatorially the following results: The 132-segmented permutations of length n with k occurrences of 132 are in one-to-one corresponden...
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We exhibit a bijection between 132-avoiding permutations and Dyck paths. Using this bijection, it is shown that all the recently discovered results on generating functions for 132-avoiding permutations with a given number of occurrences of the pattern 12 . . . k follow directly from old results on the enumeration of Motzkin paths, among which is a continued fraction result due to Flajolet. As a...
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We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection to others and exhibit a bistatistic on 231-avoiding permutations which is related to the q, t-Catalan numbers.
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A new algorithms to generate all Dyck words is presented, which is used in ranking and unranking Dyck words. We emphasize the importance of using Dyck words in encoding objects related to Catalan numbers. As a consequence of formulas used in the ranking algorithm we can obtain a recursive formula for the nth Catalan number.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2016
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.05.007