On the homology of geometric lattices

DOI10.1007/BF02483913zbMath0484.06014MaRDI QIDQ1163579

Publication date: 1982

Published in: Algebra Universalis (Search for Journal in Brave)

Whitney homology geometric lattice Whitney numbers broken circuit minimal dependent subsets neat base family order homology semi-modular point lattice of finite length

Mathematics Subject Classification ID

Partial orders, general (06A06) Nonabelian homological algebra (category-theoretic aspects) (18G50) Semimodular lattices, geometric lattices (06C10) Other homology theories in algebraic topology (55N35)

Related Items

On the free Lie algebra with multiple brackets, Algebraic and combinatorial aspects of the general theory of hypergeometric functions, Deletion-restriction for sheaf homology of graded atomic lattices, The homology of partitions with an even number of blocks, Solutions modulo \(p\) of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz, \(g\)-elements, finite buildings and higher Cohen-Macaulay connectivity., Positive Sum Systems, The determinant formula for a matroid bilinear form, Heaviside functions of a configuration of hyperplanes, Inclusion of poset homology into Lie algebra homology, Commutative algebras for arrangements, Incidence matrices, geometrical bases, combinatorial prebases and matroids, Combinatorial bases in systems of simplices and chambers, Representation stability for families of linear subspace arrangements, Topological representations of matroid maps, Eigenvectors for a random walk on a left-regular band, The homology representation of subword order, On the homology of the noncrossing partition lattice and the Milnor fibre, Deletion-restriction for subspace arrangements, On the action of the symmetric group on the free Lie algebra and the partition lattice, 𝛽𝐧𝐛𝐜-bases for cohomology of local systems on hyperplane complements, Broken circuit complexes: Factorizations and generalizations, Arrangements of hyperplanes and Lie algebra homology, Whitney duals of geometric lattices, A note on the Orlik-Solomon algebra, The Whitney duals of a graded poset, Combinatorial and algebraic structure in Orlik-Solomon algebras, A basis for the non-crossing partition lattice top homology, Hyperplane arrangement cohomology and monomials in the exterior algebra, Face numbers of Engström representations of matroids, On the (co)homology of the poset of weighted partitions, Geometric relationship between cohomology of the complement of real and complexified arrangements, Cellular cohomology of posets with local coefficients, Free Lie superalgebras, trees and chains of partitions, The reflection representation in the homology of subword order, A basis for the top homology of a generalized partition lattice, Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers, Cohomology of Dowling lattices and Lie (super)algebras, On the (co)homology of the partition lattice and the free Lie algebra., A Möbius identity arising from modularity in a matroid bilinear form, Group actions on arrangements of linear subspaces and applications to configuration spaces, Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings, Equivariant topology of configuration spaces, Algebras generated by reciprocals of linear forms, Two generalizations of posets of shuffles

Cites Work

Unnamed Item
Unnamed Item
Whitney numbers of geometric lattices
Connected matroids with the smallest Whitney numbers
Shellable and Cohen-Macaulay Partially Ordered Sets
An Inequality for the Möbius Function of a Geometric Lattice
[https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]