Results 1 to 10 of about 426,250 (213)
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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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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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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Generalized Dyck tilings (Extended Abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The first goal of
Matthieu Josuat-Vergès, Jang Soo Kim
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Rational Dyck Paths in the Non Relatively Prime Case [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We study the relationship between rational slope Dyck paths and invariant subsets in Z, extending the work of the first two authors in the relatively prime case.
Eugene Gorsky +2 more
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On rational Dyck paths and the enumeration of factor-free Dyck words [PDF]
Discrete Applied Mathematics, 2018 10 pages, 2 figures.
Michael D Weiner
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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...
C Krattenthaler
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The statistic “number of udu's” in Dyck paths
Discrete Mathematics, 2004 This paper studies the enumeration of Dyck paths by the number of \(udu\)'s (up-down-up). More precisely, the enumeration of Dyck paths with given semilength and given number of \(udu\)'s is obtained. An \(udu\) is said to be at low (high) level, if its peak is at level (greater than) one.
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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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