Results 1 to 10 of about 1,109,500 (204)
Down-step statistics in generalized Dyck paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck paths consisting of steps $\{(1, k), (1, -1)\}$ such that the path stays (weakly) above the line $y=-t$, is studied.
Andrei Asinowski +2 more
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Pattern-avoiding Dyck paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck
Antonio Bernini +3 more
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Dyck path triangulations and extendability (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce the Dyck path triangulation of the cartesian product of two simplices $\Delta_{n-1}\times\Delta_{n-1}$. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations
Cesar Ceballos +2 more
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Brauer Configuration Algebras Arising from Dyck Paths
Mathematics, 2022 The enumeration of Dyck paths is one of the most remarkable problems in Catalan combinatorics. Recently introduced categories of Dyck paths have allowed interactions between the theory of representation of algebras and cluster algebras theory. As another
Agustín Moreno Cañadas +2 more
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Applications in Enumerative Combinatorics of In finite Weighted Automata and Graphs [PDF]
Scientific Annals of Computer Science, 2014 In this paper, we present a general methodology to solve a wide variety of classical lattice path counting problems in a uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted
R. De Castro, A. Ramírez, J.L. Ramírez
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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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The location of the first maximum in the first sojourn of a Dyck path [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 For Dyck paths (nonnegative symmetric) random walks, the location of the first maximum within the first sojourn is studied. Generating functions and explicit resp. asymptotic expressions for the average are derived.
Helmut Prodinger
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