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Design and optimization of graded lattice structures with load path-oriented reinforcement
Materials & Design, 2023 Lattice structures have been increasingly used in load-carrying applications due to their exceptional mechanical performance. This study presents a novel load path methodology for designing and optimizing functionally graded lattice structures composed ...
Shengjie Zhao +4 more
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Lattice Path Bicircular Matroids
Graphs and CombinatoricsAbstractLattice path matroids and bicircular matroids are two well-known classes of transversal matroids. In the seminal work of Bonin and de Mier about structural properties of lattice path matroids, the authors claimed that lattice path matroids significantly differ from bicircular matroids.
Santiago Guzmán-Pro +2 more
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Congruence for Lattice Path Models with Filter Restrictions and Long Steps
Mathematics, 2022 We derive a path counting formula for a two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves the problem of finding an explicit formula for
Dmitry Solovyev
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Bergman Complexes of Lattice Path Matroids [PDF]
SIAM Journal on Discrete Mathematics, 2015 We give an explicit description of the poset of cells of Bergman complexes of Lattice Path Matroids and establish a criterion for its simpliciality, in terms of the shape of the bounding paths.
Emanuele Delucchi
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Lattice path matroids: The excluded minors
Journal of Combinatorial Theory Series B, 2010 13 pages, 2 ...
Joseph E Bonin
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The Carlitz lattice path polynomials
Discrete Mathematics, 2000 The author interprets some polynomials of Carlitz as generating functions for some natural statistics on lattice paths in \(\mathbb{R}^n\) \((n= 2,3)\) which admit diagonal moves.
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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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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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