Combinatorial Laplacian of the Matching Complex
by Xun Dong, Michelle L. Wachs - 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 self-conjugate. We show how the combinatorial Laplacian can be used to give an elegant proof of this result. We also show that the spectru ..."
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 self-conjugate. 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
by W. Kook, V. Reiner, D. Stanton - 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 R-vector space of (oriented) simplicial i-chains in K with r ..."
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 R-vector space of (oriented) simplicial i-chains in K
A combinatorial Laplacian with vertex weights
by F. R. K. Chung, Robert P. Langlands , 1996
"... One of the classical results in graph theory is the matrix-tree 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 ..."
One of the classical results in graph theory is the matrix-tree 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
The surjectivity of the combinatorial Laplacian on infinite graphs
by Tullio Ceccherini-silberstein, Michel Coornaert, Józef Dodziuk
"... ar ..."
Discrete combinatorial Laplacian operators for digital geometry processing
by Hao Zhang - 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 ..."
for eigenvalue decomposition, mimicking the effect of discrete Fourier analysis on mesh geometry. In this paper, we investigate matrix-theoretic properties, e.g., symmetry, stochasticity, and energy-compaction, of well-known combinatorial mesh Laplacians and examine how they would influence our choice
Small spectral gap in the combinatorial Laplacian implies Hamiltonian
by Steve Butler, Fan Chung , 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 ..."
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
by Roland Hildebrand, Stefano Mancini, Simone Severini - 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 ..."
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
by J. Friedman - 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, ", ..."
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"
by Art M. Duval
"... This is a bibliography to accompany the slides from my talk at ..."
This is a bibliography to accompany the slides from my talk at
An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z2
by Yakov Shlapentokh-rothman , 2010