Counting Segmented Permutations Using Bicoloured Dyck Paths
نویسندگان
چکیده
منابع مشابه
Counting Segmented Permutations Using Bicoloured Dyck Paths
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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The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from (0, 0) to (n, n) which is below the diagonal line y = x. One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from (0, 0) to (m, n) ∈ N2 which is below the diagonal line y...
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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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A Dyck word w is a word over the alphabet {x, x} that contains as many letters x as letters x and such that any prefix contains at least as many letters x as letters x. The size of w is the number of letters x in w. A Dyck path is a walk in the plane, that starts from the origin, is made up of rises, i.e. steps (1, 1), and falls, i.e. steps (1,−1), remains above the horizontal axis and finishes...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/1936