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Discrete Morse theory and classifying spaces [PDF]
, 2018 The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching ΞΌ on a finite regular CW complex X, Forman introduced a discrete analogue of gradient flows.
Tamaki, D +4 more
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Discrete microlocal Morse theory [PDF]
We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a
Draganov, Ondrej ; https://orcid.org/ +1 more
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Discrete Morse Theory Algorithms [PDF]
, 2017 Discrete Morse Theory (DMT) is the discrete version of Morse Theory and has been introduced by Robin Forman. Discrete Morse Theory provides a powerful tool for the analysis of topological spaces.
Nazem, Soroosh
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Generalizations of discrete Morse theory [PDF]
, 2018 We generalize Formanβs discrete Morse theory, on one end by developing a discrete analogue of Morse-Bott theory for CW complexes, motivated by Morse-Bott theory in the smooth setting. On the other, motivated by J-N.
Yaptieu Djeungue, Odette Sylvia +1 more
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The $q=-1$ phenomenon for bounded (plane) partitions via homology concentration [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Algebraic complexes whose "faces'' are indexed by partitions and plane partitions are introduced, and their homology is proven to be concentrated in even dimensions with homology basis indexed by fixed points of an involution, thereby explaining ...
P. Hersh, J. Shareshian, D. Stanton
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Discrete Morse Theory and Persistent Homology [PDF]
In this paper we explain at the theoretical level how discrete Morse theory can provide us a more efficient approach to compute persistent homologies.
Lai, Chung-Ping
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The MΓΆbius function of generalized subword order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $P$ be a poset and let $P^*$ be the set of all finite length words over $P$. Generalized subword order is the partial order on $P^*$ obtained by letting $uβ€ w$ if and only if there is a subword $u'$ of $w$ having the same length as $u$ such that ...
Peter R. W. McNamara, Bruce E. Sagan
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International Journal of Applied Earth Observations and Geoinformation, 2023 Terrestrial laser scanning (TLS) is a ground-based approach to rapidly acquire 3D point clouds via Light Detection and Ranging (LiDAR) technologies. Quantifying tree-scale structure from TLS point clouds requires segmentation, yet there is a lack of ...
Xin Xu +4 more
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Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems
Discrete Dynamics in Nature and Society, 2011 By using Morse theory, the critical point theory, and the character of πΎ1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem βΞ2π₯(πβ1)=π(π,π₯(π)),πββ€(1,π) subject to π₯(0)=
Jianmin Guo, Caixia Guo
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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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