Results 111 to 120 of about 1,109,500 (204)
Croatica Chemica Acta, 2002 A simple bijection is established between Morgan trees and Dyck paths. As a consequence, exact enumerative results for Morgan trees on given number of vertices are obtained in terms of Catalan numbers. The results are further refined by enumerating all Morgan trees with prescribed number of internal vertices and by computing the average number of ...
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On the dominance partial ordering of Dyck paths
, 2006 The lattice of Dyck paths with the dominance partial order is studied. The notions of filling and degree of a Dyck path are introduced, studied and used for the evaluation of the Möbius function and its powers.
A. Sapounakis, P. Tsikouras, I. Tasoulas
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Dyck paths and pattern-avoiding matchings
European Journal of Combinatorics, 2007 How many matchings on the vertex set V={1,2,...,2n} avoid a given configuration of three edges? Chen, Deng and Du have shown that the number of matchings that avoid three nesting edges is equal to the number of matchings avoiding three pairwise crossing edges. In this paper, we consider other forbidden configurations of size three.
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An involution on Dyck paths and its consequences
Discrete Mathematics, 1999 Dyck paths of semilength \(n\) are paths from \((0,0)\) to \((2n,0)\) with steps \(u=(1,1)\) and \(d=(1,-1)\) which lie on or above the \(x\)-axis. Many statistics of Dyck paths have been well studied, like the number of peaks (i.e. \(ud\)'s), the number of valleys (i.e. \(du\)'s), the number of doublerises (i.e. \(uu\)'s), the height of the first peak
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Enumerations and bijections of Dyck paths
A research report submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2023A Dyck path is a non-negative lattice path with the ...
Mohlala, Derrick
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, 2012 We propose an original approach to the problem of rankunimodality for Dyck lattices. It is based on a well known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of Dyck lattices into saturated chains.
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Counting Ascents in Generalized Dyck Paths.
, 2018 Non-negative Lukasiewicz paths are special two-dimensional lattice paths never passing below their starting altitude which have only one single special type of down step. They are well-known and -studied combinatorial objects, in particular due to their bijective relation to trees with given node degrees.
Hackl, Benjamin +2 more
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, 2023 We propose different ways of lifting the notion of Dyck language from words to 2-dimensional (2D) pictures, by means of new definitions of increasing comprehensiveness.
Pietro, Pierluigi San +2 more
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We answer a question of Simental by providing a combinatorial interpretation of a formula which generalizes rational Catalan numbers and which appears in the study of Springer fibers. We provide an interpretation in terms of binary necklaces as well as anchored Dyck paths.
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