Combinatorial Laplacians of matroid complexes

DOI10.1090/S0894-0347-99-00316-1zbMath0940.05021MaRDI QIDQ4700182

Woong Kook, Victor Reiner, Dennis W. Stanton

Publication date: 1 November 1999

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

spectraorthogonal decompositionmatroid complexcombinatorial Laplaciansexternal activityinternal activity

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items (21)

Topology of augmented Bergman complexes ⋮ Recurrence relations for the spectrum polynomial of a matroid ⋮ Isoperimetric inequalities in simplicial complexes ⋮ Enumerating degree sequences in digraphs and a cycle--cocycle reversing system ⋮ A formula for simplicial tree-numbers of matroid complexes ⋮ On discrete gradient vector fields and Laplacians of simplicial complexes ⋮ Truncation formulas for invariant polynomials of matroids and geometric lattices ⋮ Mixing in High-Dimensional Expanders ⋮ Critical groups of simplicial complexes ⋮ Ringel duality for perverse sheaves on hypertoric varieties ⋮ On eigenvalues of random complexes ⋮ Möbius coinvariants and bipartite edge-rooted forests ⋮ Cellular spanning trees and laplacians of cubical complexes ⋮ Matroidal Schur algebras ⋮ The combinatorial Laplacian of the Tutte complex ⋮ Kirchhoff index of simplicial networks ⋮ Simplicial matrix-tree theorems ⋮ Quasi-matroidal classes of ordered simplicial complexes ⋮ A convolution formula for the Tutte polynomial ⋮ Lattice points in orthotopes and a huge polynomial Tutte invariant of weighted gain graphs ⋮ Shifted simplicial complexes are Laplacian integral

Cites Work

• Some aspects of groups acting on finite posets
• On the Betti numbers of chessboard complexes
• External and internal elements of a matroid basis
• Computing Betti numbers via combinatorial Laplacians
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