Results 61 to 70 of about 20,234 (200)
Torus knots and generalized Schröder paths
Nuclear Physics BWe relate invariants of torus knots to the counts of a class of lattice paths, which we call generalized Schröder paths. We determine generating functions of such paths, located in a region determined by a type of a torus knot under consideration, and ...
Marko Stošić, Piotr Sułkowski
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Materials & Design, 2022 The laborious work of post-processing powder removal from lattice structures made by polymer powder-based additive manufacturing (AM) process is still a major challenge and requires in-depth study. Here, a novel 3D honeycomb shaped lattice structure with
Saurav Verma +3 more
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Half-lattice Paths and Virasoro Characters [PDF]
Fundamenta Informaticae, 2012 We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p, p′) minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the M(p, 2p ± 1) characters, reformulating them in such a way that the two cases may be treated uniformly. That the generating
Olivier Blondeau-Fournier +2 more
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Intersecting longest paths and longest cycles: A survey
Electronic Journal of Graph Theory and Applications, 2013 This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention.
Ayesha Shabbir +2 more
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Pattern-avoiding Dyck paths [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck
Antonio Bernini +3 more
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On Lattice Paths with Diagonal Steps [PDF]
Canadian Mathematical Bulletin, 1964 In [1] L. Moser and W. Zayachkowski considered lattice paths from (0, 0) to (x, y) where the possible moves are of three types: (1) a horizontal step, (2) a vertical step, and (3) a diagonal step. They obtained an expression for the number of paths from (0, 0) to (n, n) lying below the main diagonal except at the terminal points. In this note we extend
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Mathematical Communications, 2016 Consider an $m\times n$ table $T$ and latices paths $ν_1,\ldots,ν_k$ in $T$ such that each step $ν_{i+1}-ν_i=(1,1)$, $(1,0)$ or $(1,-1)$. The number of paths from the $(1,i)$-blank (resp. first column) to the $(s,t)$-blank is denoted by $\mathcal{D}^i(s,t)$ (resp. $\mathcal{D}(s,t)$).
Yaqubi, Daniel +2 more
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The Excluded Minors for Lattice Path Polymatroids
The Electronic Journal of Combinatorics, 2022 We find the excluded minors for the minor-closed class of lattice path polymatroids as a subclass of the minor-closed class of Boolean polymatroids. Like lattice path matroids and Boolean polymatroids, there are infinitely many excluded minors, but they fall into a small number of easily-described types.
Joseph E. Bonin, Carolyn Chun, Tara Fife
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Optimal Embedding of Graphs with Nonconcurrent Longest Paths in Archimedean Tessellations
Complexity, 2023 Optimal graph embeddings represent graphs in a lower dimensional space in a way that preserves the structure and properties of the original graph. These techniques have wide applications in fields such as machine learning, data mining, and network ...
Muhammad Faisal Nadeem +2 more
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Smooth Paths on Three-Dimensional Lattice [PDF]
Physical Review Letters, 1994 7 pages,NUP-A-94 ...
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