Generalized Dyck equations and multilabel trees
نویسندگان
چکیده
منابع مشابه
Generalized Dyck equations and multilabel trees
New topological operations are introduced in order to recover the generalized Dyck equations presented by D. Arquès et al. in another way for the generating functions of maps and colored maps, by decomposing maps topologically and bijectively. By repeatedly applying the operations which made it possible to reveal the generalized Dyck equations for the successive transformed maps, oneto-one corr...
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The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from (0, 0) to (n, n) which is below the diagonal line y = x. One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from (0, 0) to (m, n) ∈ N2 which is below the diagonal line y...
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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 this work is to give an alternative point of view on Dyck tilings by making use of the weak order and the Bruhat order on permutations. Then w...
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In 2009, Shapiro posed the following question: “What is the asymptotic proportion of Dyck paths having an even number of hills?” In this paper, we answer Shapiro’s question, as well as a generalization of the question to ternary paths. We find that the probability that a randomly chosen ternary path has an even number of hills approaches 125/169 as the length of the path approaches infinity. Ou...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.05.017