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Meanders and Dyck-path billiards
RAIRO - Theoretical Informatics and ApplicationsWe study a statistic traj on the ordered pairs (P,Q) of Dyck paths of size n, which counts the number of billiard trajectories in the grid polygon enclosed by P and Q, where Q is the path obtained by reflecting Q over the ground line.
Eu, Sen-Peng;Fu, Tung-Shan;Hsu, Hsiang-Chun
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Skew Dyck paths with catastrophes [PDF]
Discrete Mathematics Letters, 2022 Skew Dyck paths are like Dyck paths, but an additional south-west step $(-1,-1)$ is allowed, provided that the path does not intersect itself. Lattice paths with catastrophes can drop from any level to the origin in just one step. We combine these two ideas. The analysis is strictly based on generating functions, and the kernel method is used.
Helmut Prodinger
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Discrete Mathematics, 1990 It is well known (see [3, 6, 9, 10, 11]) that Dyck paths are in bijection with “Dyck words”, “ballot sequences”, “well formed sequences of parentheses”, “2-lines standard-tableaux”, “binary trees”, “ordered trees”; all these are counted by Catalan ...
Yeh, Yeong-Nan, Labelle, Jacques
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Dyck paths, Motzkin paths and traffic jams [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2004 It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the asymmetric exclusion process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path
Blythe, R A +6 more
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Fungal-Bacterial Interactions in Polymicrobial Infections: Hidden Threats. [PDF]
MicrobiologyopenABSTRACT Polymicrobial infections involving fungi and bacteria represent a major and increasingly recognized clinical challenge, in which interkingdom interactions significantly amplify disease severity, antimicrobial resistance, and treatment failure. Rather than passive co‐existence, fungal–bacterial communities form highly coordinated systems driven
Gourabi MJR +3 more
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Generating functions for a lattice path model introduced by Deutsch
Special Matrices, 2021 The lattice path model suggested by E. Deutsch is derived from ordinary Dyck paths, but with additional down-steps of size −3, −5, −7, . . . . For such paths, we find the generating functions of them, according to length, ending at level i, both, when ...
Prodinger Helmut
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Area of Brownian Motion with Generatingfunctionology [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 This paper gives a survey of the limit distributions of the areas of different types of random walks, namely Dyck paths, bilateral Dyck paths, meanders, and Bernoulli random walks, using the technology of generating functions only.
Michel Nguyên Thê
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Rational Catalan Combinatorics: The Associahedron [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Each positive rational number $x>0$ can be written $\textbf{uniquely}$ as $x=a/(b-a)$ for coprime positive integers ...
Drew Armstrong +2 more
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Combinatorial Generation Algorithms for Some Lattice Paths Using the Method Based on AND/OR Trees
Algorithms, 2023 Methods of combinatorial generation make it possible to develop algorithms for generating objects from a set of discrete structures with given parameters and properties.
Yuriy Shablya
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A Bijection on Bilateral Dyck Paths [PDF]
Australas. J Comb., 2012 revised ...
Paul R. G. Mortimer, Thomas Prellberg
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