Results 101 to 110 of about 1,383 (202)
On Enumeration of Dyck Paths with colored hills
J. Integer Seq., 2018 We continue to investigate the properties of the earlier defined functions fm and gm, which depend on an initial arithmetic function f0. In this papers values of f0 are the Fine numbers. We investigate functions fi; gi; (i = 1; 2; 3; 4). For each function, we derive an explicit formula and give a combinatorial interpretation.
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Bicoloured Dyck paths and the contact polynomial for n non-intersecting paths in a half-plane lattice [PDF]
, 2003 In this paper configurations of n non-intersecting lattice paths which begin and endontheliney = 0 and are excluded from the region below this line are considered. Such configurations are called Hankel n-paths and their contact polynomial is defined by
Essam, J W +3 more
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Permutations with Restricted Patterns and Dyck Paths
Advances in Applied Mathematics, 2001 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...
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On the dominance partial ordering of Dyck paths
, 2006 The lattice of Dyck paths with the dominance partial order is studied. The notions of filling and degree of a Dyck path are introduced, studied and used for the evaluation of the Möbius function and its powers.
A. Sapounakis, P. Tsikouras, I. Tasoulas
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Croatica Chemica Acta, 2002 A simple bijection is established between Morgan trees and Dyck paths. As a consequence, exact enumerative results for Morgan trees on given number of vertices are obtained in terms of Catalan numbers. The results are further refined by enumerating all Morgan trees with prescribed number of internal vertices and by computing the average number of ...
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Short note on the number of 1-ascents in dispersed Dyck paths
, 2017 A dispersed Dyck path (DDP) of length [Formula: see text] is a lattice path on [Formula: see text] from [Formula: see text] to [Formula: see text] in which the following steps are allowed: “up” [Formula: see text]; “down” [Formula: see text]; and “right”
Kairi Kangro +2 more
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On \({k}\)-Dyck Paths with a Negative Boundary
Journal of Combinatorial Mathematics and Combinatorial ComputingPaths that consist of up-steps of one unit and down-steps of \(k\) units, being bounded below by a horizontal line \(-t\), behave like \(t+1\) ordered tuples of \(k\)-Dyck paths, provided that \(t\le k\). We describe the general case, allowing \(t\) also to be larger. Arguments are bijective and/or analytic.
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Counting segmented permutations using bicoloured Dyck paths
, 2005 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).
Claesson, Anders
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Counting segmented permutations using bicoloured Dyck paths
, 2008 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).
Anders Claesson
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MIN-turns and MAX-turns in k-Dyck paths: a pure generating function approach
, 2023 $k$-Dyck paths differ from ordinary Dyck paths by using an up-step of length $k$. We analyze at which level the path is after the $s$-th up-step and before the $(s+1)$st up-step.
Prodinger, Helmut
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