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1,070,283
On optimizing discrete Morse functions
, 2003
"... Abstract. Forman introduced discrete Morse theory as a tool for studying CW complexes by collapsing them onto smaller, simplertounderstand complexes of critical cells in [Fo]. Chari reformulated discrete Morse theory for regular cell complexes in terms of acyclic matchings on face posets in [Ch]. ..."
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Cited by 9 (2 self)
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]. This paper addresses two questions: (1) under what conditions may several gradient paths in a discrete Morse function simultaneously be reversed to cancel several pairs of critical cells, to further collapse the complex, and (2) how to use lexicographically first reduced expressions for permutations (in
Constructing Discrete Morse Functions
, 2002
"... Morse theory has been considered a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It o ..."
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Cited by 8 (3 self)
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Morse theory has been considered a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes
Discrete Morse functions from Fourier transforms
, 2007
"... A discrete Morse function for a simplicial complex describes how to construct a homotopy equivalent CWcomplex with hopefully fewer cells. We associate a boolean function with the simplicial complex and construct a discrete Morse function using its Fourier transform. Methods from theoretical compute ..."
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Cited by 5 (0 self)
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A discrete Morse function for a simplicial complex describes how to construct a homotopy equivalent CWcomplex with hopefully fewer cells. We associate a boolean function with the simplicial complex and construct a discrete Morse function using its Fourier transform. Methods from theoretical
Computing Optimal Discrete Morse Functions (Extended Abstract)
, 2004
"... The essential structural information of discrete Morse functions is captured by socalled Morse matchings. We show that computing optimal Morse matchings is N Phard and give an integer programming formulation for the problem. Then we present first polyhedral results for the corresponding polytope a ..."
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Cited by 4 (0 self)
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The essential structural information of discrete Morse functions is captured by socalled Morse matchings. We show that computing optimal Morse matchings is N Phard and give an integer programming formulation for the problem. Then we present first polyhedral results for the corresponding polytope
Optimal discrete Morse functions for 2manifolds
 Computational Geometry: Theory and Applications
, 2003
"... Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several c ..."
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Cited by 24 (6 self)
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discrete Morse functions on discrete 2manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality.
Discrete Morse functions from lexicographic orders
 Trans. Amer. Math. Soc
"... Abstract. This paper shows how to construct a discrete Morse function with a relatively small number of critical cells for the order complex of any finite poset with ˆ0 andˆ1 from any lexicographic order on its maximal chains. Specifically, if we attach facets according to the lexicographic order on ..."
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Cited by 25 (5 self)
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Abstract. This paper shows how to construct a discrete Morse function with a relatively small number of critical cells for the order complex of any finite poset with ˆ0 andˆ1 from any lexicographic order on its maximal chains. Specifically, if we attach facets according to the lexicographic order
POLYHEDRAL REPRESENTATION OF DISCRETE MORSE FUNCTIONS ON REGULAR CW COMPLEXES AND POSETS
"... Abstract. It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a represent ..."
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Cited by 1 (0 self)
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Abstract. It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a
Tight complexes in 3space admit perfect discrete Morse functions
, 2012
"... In 1967, Chillingworth proved that all convex simplicial 3balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that all tight simplicial 3manifolds admit some perfect discrete Morse function. We also strengthen Chillingworth’s theorem b ..."
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Cited by 1 (1 self)
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In 1967, Chillingworth proved that all convex simplicial 3balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that all tight simplicial 3manifolds admit some perfect discrete Morse function. We also strengthen Chillingworth’s theorem
Persistence simplification of discrete Morse functions on surfaces (Oberwolfach report)
"... We apply the concept of persistent homology [1] to Forman’s discrete Morse theory [2] on regular 2manifold CW complexes and solve the problem of minimizing the number of critical points among all functions within a prescribed distance δ from a given input function. Our result achieves a lower bound ..."
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We apply the concept of persistent homology [1] to Forman’s discrete Morse theory [2] on regular 2manifold CW complexes and solve the problem of minimizing the number of critical points among all functions within a prescribed distance δ from a given input function. Our result achieves a lower
Results 1  10
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1,070,283