Results 11 to 20 of about 1,109,500 (204)
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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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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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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Left to right maxima in Dyck prefixes [PDF]
, 2023 In a Dyck path, a peak which is strictly (weakly) higher than all the preceding peaks is called a strict (weak) left-to-right maximum. By dropping the restrictions for the path to end on the $x$-axis, one obtains Dyck prefixes.We obtain explicit ...
Knopfmacher, Arnold, Blecher, Aubrey
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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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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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