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Discrete Mathematics, 1999 An elementary technique is used for the enumeration of Dyck paths according to various parameters. For several of the considered parameters the generating function is expressed in terms of the Narayana function.
Deutsch, Emeric
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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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Enumerative Combinatorics of Intervals in the Dyck Pattern Poset [PDF]
Order, 2021 We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations.
Antonio Bernini +2 more
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Discrete Mathematics, 2014 International audienceWe introduce the notion of 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 ...
Axel Bacher +2 more
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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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MIN-turns and MAX-turns in k-Dyck paths: A pure generating function approach [PDF]
Notes on Number Theory and Discrete Mathematicsk-Dyck paths differ from ordinary Dyck paths by using an up-step of length k. We analyze at which level the path is after the s-th up-step and before the (s+1)-st up-step.
Helmut Prodinger
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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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