Results 1 to 10 of about 1,064,332 (196)
Discrete Mathematics, 1999 Dyck paths of semilength \(n\) are paths from (0, 0) to \((2n,0)\) with steps (1, 1) and \((1,-1)\) which lie on or above the \(x\)-axis. The paper gives a systematic treatment to the enumeration of Dyck paths according to semilength and one more statistics.
Deutsch, Emeric
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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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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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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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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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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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Dyck path triangulations and extendability
Journal of Combinatorial Theory - Series A, 2015 We introduce the Dyck path triangulation of the cartesian product of two simplices $Δ_{n-1}\timesΔ_{n-1}$. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations of $Δ_{r\ n-1}\timesΔ_{n-1}$ using rational Dyck paths. Our study of the Dyck path triangulation is motivated
Cesar Ceballos
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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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