Results 11 to 20 of about 426,250 (213)
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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Given a positive rational $q$, we consider Dyck paths having height at most two with some constraints on the number of consecutive peaks and consecutive valleys, depending on $q$. We introduce a general class of Dyck paths, called rational Dyck paths, and provide the associated generating function, according to their semilength, as well as the ...
Barcucci E. +3 more
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Dyck paths with coloured ascents [PDF]
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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Grand Dyck paths with air pockets
The Art of Discrete and Applied Mathematics, 2023 Grand Dyck paths with air pockets (GDAP) are a generalization of Dyck paths with air pockets by allowing them to go below the $x$-axis. We present enumerative results on GDAP (or their prefixes) subject to various restrictions such as maximal/minimal height, ordinate of the last point and particular first return decomposition.
Baril, Jean-Luc +3 more
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Dyck paths of knight moves [PDF]
Discrete Applied Mathematics, 1989 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jacques Labelle, Yeong-Nan Yeh
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Dyck paths, Motzkin paths, and the binomial transform [PDF]
J. Integer Seq., 2015 Summary: We study the moments of orthogonal polynomial sequences (OPS) arising from tridiagonal matrices. We obtain combinatorial information about the sequence of moments of some OPS in terms of Motzkin and Dyck paths, and also in terms of the binomial transform. We then introduce an equivalence relation on the set of Dyck paths and some operations on
CAPPARELLI, Stefano, DEL FRA, ALBERTO
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Dispersed Dyck paths revisited [PDF]
Contributions to MathematicsDispersed Dyck paths are Dyck paths, with possible flat steps on level 0. We revisit and augment questions about them from the Encyclopedia of Integer Sequences, in a systematic way that uses generating functions and the kernel ...
Helmut Prodinger
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Dyck path triangulations and extendability (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce the Dyck path triangulation of the cartesian product of two simplices $\Delta_{n-1}\times\Delta_{n-1}$. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations
Cesar Ceballos +2 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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The $m$-Cover Posets and the Strip-Decomposition of $m$-Dyck Paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 In the first part of this article we present a realization of the $m$-Tamari lattice $\mathcal{T}_n^{(m)}$ in terms of $m$-tuples of Dyck paths of height $n$, equipped with componentwise rotation order. For that, we define the $m$-cover poset $\mathcal{P}
Myrto Kallipoliti, Henri Mühle
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