Results 11 to 20 of about 20,234 (200)
Enumerating a class of lattice paths
Discrete Mathematics, 2003 Let D0(n) denote the set of lattice paths in the xy-plane that begin at (0,0), terminate at (n,n), never rise above the line y=x and have step set S={(k,0):k∈N+}∪{(0,k):k∈N+}.
Curtis Coker, Coker, Curtis
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Underdiagonal lattice paths with unrestricted steps
Discrete Applied Mathematics, 1999 We use some combinatorial methods to study underdiagonal paths (on the Z2 lattice) made up of unrestricted steps, i.e., ordered pairs of non-negative integers.
Donatella Merlini, Renzo Sprugnoli
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The ascent lattice on Dyck paths
The Electronic Journal of Combinatorics35 pagesInternational audienceIn the Stanley lattice defined on Dyck paths of size $n$, cover relations are obtained by replacing a valley $DU$ by a peak $UD$. We investigate a greedy version of this lattice, first introduced by Chenevi\`ere, where cover
Baril, Jean-Luc +3 more
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Lattice paths and generalized cluster complexes
Journal of Combinatorial Theory - Series A, 2008 In this paper we propose a variant of the generalized Schröder paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This generalization turns out to be reasonable, as attested by the connection with the faces of
Sen-Peng Eu, Tung-Shan Fu
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Lattice paths moments by cut and paste
Advances in Applied Mathematics, 2003 In the coordinate plane consider those lattice paths whose step types consist of (1, 1), (1,−1), and perhaps one or more horizontal steps. For the set of such paths running from (0, 0) to (n+ 2, 0) and remaining strictly elevated above the horizontal ...
Rinaldi S. +7 more
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Tableau stabilization and lattice paths [PDF]
Journal of Combinatorics, 2022 If one attaches shifted copies of a skew tableau to the right of itself and rectifies, at a certain point the copies no longer experience vertical slides, a phenomenon called tableau stabilization. While tableau stabilization was originally developed to construct the sufficiently large rectangular tableaux fixed by given powers of promotion, the ...
Ahlbach, Connor +3 more
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Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by
Hanna Mularczyk
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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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Combinatorics on lattice paths in strips [PDF]
European Journal of Combinatorics, 2021 For lattice paths in strips which begin at $(0,0)$ and have only up steps $U: (i,j) \rightarrow (i+1,j+1)$ and down steps $D: (i,j)\rightarrow (i+1,j-1)$, let $A_{n,k}$ denote the set of paths of length $n$ which start at $(0,0)$, end on heights $0$ or $-1$, and are contained in the strip $-\lfloor\frac{k+1}{2}\rfloor \leq y \leq \lfloor\frac{k}{2 ...
Nancy S. S. Gu, Helmut Prodinger
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Counting Lattice Paths by Using Difference Equations with Non-constant Coefficients
Известия Иркутского государственного университета: Серия "Математика", 2023 The lattice paths can be counted by the virtue of their step vectors that are aligned to the positive octant. A path can go from one point to an infinite others if there is no restriction applied such that each point only has finitely many predecessors ...
S. Chandragiri
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