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Nontrivial solutions of discrete Kirchhoff-type problems via Morse theory [PDF]
Advances in Nonlinear Analysis, 2022 In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory.
Long Yuhua
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Discrete Morse theory for the collapsibility of supremum sections [PDF]
, 2018 The Dushnik-Miller dimension of a poset $\le$ is the minimal number $d$ of linear extensions $\le_1, \ldots , \le_d$ of $\le$ such that $\le$ is the intersection of $\le_1, \ldots , \le_d$.
Balthazar Bauer, Lucas Isenmann
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Topology of matching complexes of complete graphs via discrete Morse theory [PDF]
Discrete Mathematics & Theoretical Computer ScienceBouc (1992) first studied the topological properties of $M_n$, the matching complex of the complete graph of order $n$, in connection with Brown complexes and Quillen complexes. Bj\"{o}rner et al. (1994) showed that $M_n$ is homotopically $(\nu_n-1)$
Anupam Mondal +2 more
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Combinatorial realization of the Thom-Smale complex via discrete Morse theory [PDF]
, 2010 20 pagesIn the case of smooth manifolds, we use Forman's discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function.
Étienne Gallais
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Persistent homology of unweighted complex networks via discrete Morse theory. [PDF]
Sci Rep, 2019 Kannan H, Saucan E, Roy I, Samal A.
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Fundamental theorems of Morse theory on posets
AIMS Mathematics, 2022 We prove a version of the fundamental theorems of Morse theory in the setting of finite partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the Morse-Pitcher inequalities in ...
D. Fernández-Ternero +3 more
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The Elser nuclei sum revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Fix a finite undirected graph $\Gamma$ and a vertex $v$ of $\Gamma$. Let $E$ be the set of edges of $\Gamma$. We call a subset $F$ of $E$ pandemic if each edge of $\Gamma$ has at least one endpoint that can be connected to $v$ by an $F$-path (i.e., a ...
Darij Grinberg
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Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems
Electronic Research Archive, 2022 In this paper, we study discrete elliptic Dirichlet problems. Applying a variational technique together with Morse theory, we establish several results on the existence and multiplicity of nontrivial solutions.
Yuhua Long, Huan Zhang
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Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems
Advances in Difference Equations, 2007 An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.
Bo Zheng
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Merging Discrete Morse Vector Fields: A Case of Stubborn Geometric Parallelization
Algorithms, 2021 We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field V is generated using a fixed algorithm
Douglas Lenseth, Boris Goldfarb
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