Results 21 to 30 of about 1,383 (202)
Patterns in Shi Tableaux and Dyck Paths [PDF]
Order, 2021 to apper in ...
Myrto Kallipoliti +2 more
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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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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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Minimal and maximal plateau lengths in Motzkin paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 The minimal length of a plateau (a sequence of horizontal steps, preceded by an up- and followed by a down-step) in a Motzkin path is known to be of interest in the study of secondary structures which in turn appear in mathematical biology. We will treat
Helmut Prodinger, Stephan Wagner
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Bijections for lattice paths between two boundaries [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We prove that on the set of lattice paths with steps $N=(0,1)$ and $E=(1,0)$ that lie between two boundaries $B$ and $T$, the two statistics `number of $E$ steps shared with $B$' and `number of $E$ steps shared with $T$' have a symmetric joint ...
Sergi Elizalde, Martin Rubey
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Left to right maxima in Dyck prefixes
, 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 sandpile model, polyominoes, and a $q,t$-Narayana polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We give a polyomino characterisation of recurrent configurations of the sandpile model on the complete bipartite graph $K_{m,n}$ in which one designated vertex is the sink.
Mark Dukes, Yvan Le Borgne
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