Whitney Number Inequalities for Geometric Lattices

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial inequalities (05A20) Combinatorial aspects of matroids and geometric lattices (05B35) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (33)

The Broken-Circuit Complex ⋮ Classifications of finite highly transitive dimensional linear spaces ⋮ Top-heavy phenomena for transformations ⋮ Constructible Sheaf Complexes in Complex Geometry and Applications ⋮ The Kazhdan-Lusztig polynomial of a matroid ⋮ Cartesian lattice counting by the vertical 2-sum ⋮ Degenerate \(r\)-Whitney numbers and degenerate \(r\)-Dowling polynomials via boson operators ⋮ On the ``log rank-conjecture in communication complexity ⋮ The work of June Huh ⋮ Some properties of characteristic polynomials and applications to T- lattices ⋮ Essence of independence: Hodge theory of matroids since June Huh ⋮ The Slimmest Geometric Lattices ⋮ Combinatorics and Hodge theory ⋮ Combinatorial geometry takes the lead ⋮ A flag Whitney number formula for matroid Kazhdan-Lusztig polynomials ⋮ Applications of lattice theory to graph decomposition ⋮ The independent sets of rank k of a matroid ⋮ A proof of a consequence of Dirac's conjecture ⋮ Matching in modular lattices ⋮ Consistent dually semimodular lattices ⋮ Matchings and Radon transforms in lattices II. Concordant sets ⋮ Complementing permutations in finite lattices ⋮ Right \(l\)-groups, geometric Garside groups, and solutions of the quantum Yang-Baxter equation ⋮ The Radon transforms of a combinatorial geometry, I ⋮ Modular Constructions for Combinatorial Geometries ⋮ On the unimodality of the independent set numbers of a class of matroids ⋮ On the lines-planes inequality for matroids ⋮ Pairings from down-sets and up-sets in distributive lattices ⋮ The slimmest arrangements of hyperplanes: II. Basepointed geometric lattices and Euclidean arrangements ⋮ Communication complexity and combinatorial lattice theory ⋮ Coloring complexes and combinatorial Hopf monoids ⋮ Matchings and Radon transforms in lattices. I: Consistent lattices ⋮ Communication complexity in lattices

Cites Work

Proof of a conjecture on finite modular lattices
The Slimmest Geometric Lattices
A Catalogue of Combinatorial Geometries
Stirling Behavior is Asymptotically Normal
Concavity properties and a generating function for stirling numbers
On the Foundations of Combinatorial Theory II. Combinatorial Geometries
A rank inequality for finite geometric lattices
[https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
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