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Discrete Mathematics, 1990 Let \({\mathcal S}\) be a finite multi-set (a set with repetitions) of vectors in \({\mathbb{N}}\times {\mathbb{N}}\) and let \({\mathcal S}^*=\{(r,-s)+(r,s)\in {\mathcal S}\}.\) An A-path (\({\mathcal S}\)-Dyck path) is a path in \({\mathbb{Z}}\times {\mathbb{Z}}\) which starts from (0,0) and ends on the x-axis, uses only vectors from \({\mathcal S}+{\
Jacques Labelle, Yeong-Nan Yeh
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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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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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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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Dyck paths, Motzkin paths and traffic jams [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2004 It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths.
Blythe, R. A. +3 more
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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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A Bijection on Bilateral Dyck Paths
Australas. J Comb., 2012 revised ...
Paul R. G. Mortimer, Thomas Prellberg
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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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Patterns in matchings and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs.
Jonathan Bloom, Sergi Elizalde
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Dyck paths with coloured ascents
European Journal of Combinatorics, 2008 We introduce a notion of Dyck paths with coloured ascents. For several ways of colouring, we establish bijections between sets of such paths and other combinatorial structures, such as non-crossing trees, dissections of a convex polygon, etc. In some cases enumeration gives new expression for sequences enumerating these structures.
Andrei Asinowski, Toufik Mansour
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