On the Betti numbers of chessboard complexes

DOI10.1023/A:1008693929682zbMath0914.55013MaRDI QIDQ1272900

Joel Friedman, Philip J. Hanlon

Publication date: 15 June 1999

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

representationhomology groupconnectivitygroup actionLaplacian eigenvalueBetti numberchessboard complexHodge theoryabstract simplicial complexrook configuration

Mathematics Subject Classification ID

Other designs, configurations (05B30) Equivariant homology and cohomology in algebraic topology (55N91) Abstract complexes in algebraic topology (55U05)

Related Items

Topology of bounded-degree graph complexes., Representation stability for syzygies of line bundles on Segre-Veronese varieties, Generalized chessboard complexes and discrete Morse theory, Torsion in the matching complex and chessboard complex, The graph minor theorem in topological combinatorics, The facet ideals of chessboard complexes, Critical groups of simplicial complexes, An Explicit, Characteristic-Free, Equivariant Homology Equivalence Between Koszul Complexes, On the 3-torsion part of the homology of the chessboard complex, On the representation theory of the symmetric groups., On eigenvalues of random complexes, Multiple chessboard complexes and the colored Tverberg problem, Exact sequences for the homology of the matching complex, Cellular spanning trees and laplacians of cubical complexes, Chessboard complexes indomitable, Matching complexes, bounded degree graph complexes, and weight spaces of \(\mathrm{GL}_n\)-complexes, Cycle-free chessboard complexes and symmetric homology of algebras, A Tverberg type theorem for matroids, Combinatorial Laplacians of matroid complexes, Five-torsion in the homology of the matching complex on 14 vertices, Shelling Coxeter-like complexes and sorting on trees, Simplicial matrix-tree theorems, Minimal resolutions and the homology of matching and chessboard complexes, The facet ideals of matching complexes of line graphs, Matching complexes of trees and applications of the matching tree algorithm, Shifted simplicial complexes are Laplacian integral

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Random shuffles and group representations
• The colored Tverberg's problem and complexes of injective functions
• Minimal eigenvalue of the Coxeter Laplacian for the symmetric group
• A random walk on the rook placements on a Ferrers board
• Harmonic functions and boundary value problems on a chain complex
• Finite-Difference Approach to the Hodge Theory of Harmonic Forms
• Chessboard Complexes and Matching Complexes
• On Cayley graphs on the symmetric group generated by transpositions