Results 11 to 20 of about 1,064,332 (196)
Meanders and Dyck-Path Billiards
RAIRO - Theoretical Informatics and ApplicationsWe study a statistic traj on the ordered pairs (P,Q) of Dyck paths of size n, which counts the number of billiard trajectories in the grid polygon enclosed by P and −Q, where −Q is the path obtained by reflecting Q over the ground line. In terms of grid polygon, we establish an involution on the set of such ordered pairs (P,Q) which either increases or
Sen-Peng Eu +2 more
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Rational Catalan Combinatorics: The Associahedron [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Each positive rational number $x>0$ can be written $\textbf{uniquely}$ as $x=a/(b-a)$ for coprime positive integers ...
Drew Armstrong +2 more
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Combinatorial Generation Algorithms for Some Lattice Paths Using the Method Based on AND/OR Trees
Algorithms, 2023 Methods of combinatorial generation make it possible to develop algorithms for generating objects from a set of discrete structures with given parameters and properties.
Yuriy Shablya
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The $(m, n)$-rational $q, t$-Catalan polynomials for $m=3$ and their $q, t$-symmetry [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area; skip; dinv) are given, we have an algorithm to construct the marked ...
Ryan Kaliszewski, Huilan Li
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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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Patterns in Shi Tableaux and Dyck Paths [PDF]
Order, 2021 to apper in ...
Myrto Kallipoliti +2 more
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Bijection between 20-Dyck path and ternary tree [PDF]
Journal of Hebei University of Science and TechnologyIn order to expand the basic theory of Dyck path and ternary tree, the bijection and counting problems between the 20-Dyck path and the ternary tree with n inliers were studied.
Jiahe WANG +3 more
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Dyck tilings, linear extensions, descents, and inversions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths.
Jang Soo Kim +3 more
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On Generalized Dyck Paths [PDF]
The Electronic Journal of Combinatorics, 2011 We generalize the elegant bijective proof of the Chung Feller theorem from a paper of Young-Ming Chen [The Chung-Feller theorem revisited, Disc. Math. 308 (2008), 1328–1329].
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Permutations and Pairs of Dyck Paths [PDF]
ISRN Combinatorics, 2013 We define a map v between the symmetric group Sn and the set of pairs of Dyck paths of semilength n. We show that the map v is injective when restricted to the set of 1234-avoiding permutations and characterize the image of this map.
BARNABEI, MARILENA +2 more
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