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Combinatorial Laplacian of the Matching Complex
 J. COMBIN
, 2000
"... A striking result of Bouc gives the decomposition of the representation of the symmetric group on the homology of the matching complex into irreducibles that are selfconjugate. We show how the combinatorial Laplacian can be used to give an elegant proof of this result. We also show that the spectru ..."
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Cited by 17 (1 self)
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A striking result of Bouc gives the decomposition of the representation of the symmetric group on the homology of the matching complex into irreducibles that are selfconjugate. We show how the combinatorial Laplacian can be used to give an elegant proof of this result. We also show
Combinatorial Laplacians of matroid complexes
 J. Amer. Math. Soc
, 1997
"... For any finite simplicial complex K, one can define Laplace operators ∆i which are combinatorial analogues of the Laplace operators on differential forms for a Riemannian manifold. The definition (as in [6, 7]) is as follows. Let Ci be the Rvector space of (oriented) simplicial ichains in K with r ..."
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Cited by 19 (4 self)
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For any finite simplicial complex K, one can define Laplace operators ∆i which are combinatorial analogues of the Laplace operators on differential forms for a Riemannian manifold. The definition (as in [6, 7]) is as follows. Let Ci be the Rvector space of (oriented) simplicial ichains in K
A combinatorial Laplacian with vertex weights
, 1996
"... One of the classical results in graph theory is the matrixtree theorem which asserts that the determinant of a cofactor of the combinatorial Laplacian is equal to the number of spanning trees in a graph (see [1, 7, 11, 15]). The usual notion of the combinatorial Laplacian for a graph involves edge ..."
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Cited by 30 (3 self)
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One of the classical results in graph theory is the matrixtree theorem which asserts that the determinant of a cofactor of the combinatorial Laplacian is equal to the number of spanning trees in a graph (see [1, 7, 11, 15]). The usual notion of the combinatorial Laplacian for a graph involves edge
Discrete combinatorial Laplacian operators for digital geometry processing
 in SIAM Conference on Geometric Design, 2004
, 2004
"... Abstract. Digital Geometry Processing (DGP) is concerned with the construction of signal processing style algorithms that operate on surface geometry, typically specified by an unstructured triangle mesh. An active subfield of study involves the utilization of discrete mesh Laplacian operators for e ..."
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Cited by 24 (3 self)
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for eigenvalue decomposition, mimicking the effect of discrete Fourier analysis on mesh geometry. In this paper, we investigate matrixtheoretic properties, e.g., symmetry, stochasticity, and energycompaction, of wellknown combinatorial mesh Laplacians and examine how they would influence our choice
Small spectral gap in the combinatorial Laplacian implies Hamiltonian
, 2006
"... We consider the spectral and algorithmic aspects of the problem of finding a Hamiltonian cycle in a graph. We show that a sufficient condition for a graph being Hamiltonian is that the eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph. An algorithm ..."
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Cited by 6 (1 self)
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We consider the spectral and algorithmic aspects of the problem of finding a Hamiltonian cycle in a graph. We show that a sufficient condition for a graph being Hamiltonian is that the eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph. An algorithm
Combinatorial laplacians and positivity under partial transpose
 Math. Struct. in Comp. Sci
"... Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability can ..."
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Cited by 4 (3 self)
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Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein et al. Phys. Rev. A, 73:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix carries a block structure with respect to which properties such as separability
Computing Betti Numbers via Combinatorial Laplacians
 ALGORITHMICA
, 1998
"... We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a number of advantages over other methods, both in theory and in practice. It requires small storage space in many cases. It seems to run quickly in practice, but its running time depends on a ratio, ”, ..."
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Cited by 50 (1 self)
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We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a number of advantages over other methods, both in theory and in practice. It requires small storage space in many cases. It seems to run quickly in practice, but its running time depends on a ratio
Bibliography to accompany "Combinatorial Laplacians"
"... This is a bibliography to accompany the slides from my talk at ..."
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