Results 121 to 130 of about 426,250 (213)
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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Symmetric and asymmetric peaks or valleys in (partial) Dyck paths [PDF]
Enumerative Combinatorics and Applications, 2022 Yidong Sun, Wenle Shi, Di Zhao
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Dyck paths and pattern-avoiding matchings
European Journal of Combinatorics, 2007 How many matchings on the vertex set V={1,2,...,2n} avoid a given configuration of three edges? Chen, Deng and Du have shown that the number of matchings that avoid three nesting edges is equal to the number of matchings avoiding three pairwise crossing edges. In this paper, we consider other forbidden configurations of size three.
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Article 06.1.5 Statistics on Dyck Paths
, 2008 In this paper we consider several statistics on the set of Dyck paths. Enumeration of Dyck paths according to length and various other parameters has been studied in several papers.
Toufik Mansour
core
An involution on Dyck paths and its consequences
Discrete Mathematics, 1999 Dyck paths of semilength \(n\) are paths from \((0,0)\) to \((2n,0)\) with steps \(u=(1,1)\) and \(d=(1,-1)\) which lie on or above the \(x\)-axis. Many statistics of Dyck paths have been well studied, like the number of peaks (i.e. \(ud\)'s), the number of valleys (i.e. \(du\)'s), the number of doublerises (i.e. \(uu\)'s), the height of the first peak
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Lattice Paths for Persistent Diagrams. [PDF]
Interpret Mach Intell Med Image Comput Topogr Data Anal Appl Med Data (2021), 2021 Chung MK, Ombao H.
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Enumerations and bijections of Dyck paths
A research report submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2023A Dyck path is a non-negative lattice path with the ...
Mohlala, Derrick
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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
core
, 2012 We propose an original approach to the problem of rankunimodality for Dyck lattices. It is based on a well known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of Dyck lattices into saturated chains.
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Generalization of a formula for marked plane trees
The American Journal of CombinatoricsDeutsch, Munarin and Rinaldi derived a formula for counting marked plane trees while investigating the enumeration of skew Dyck paths. The formula involves the Catalan numbers, which count plane trees among other classical combinatorial structures.
Albert Oloo Nyariaro +2 more
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