Concepts of dimension for convex geometries

DOI10.1137/23m1559853MaRDI QIDQ6552469

William T. jun. Trotter, Kolja Knauer

Publication date: 8 June 2024

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

dimensionpartially ordered setconvex geometrystandard example

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Combinatorics of partially ordered sets (06A07)

Cites Work

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• The proof of the removable pair conjecture for fractional dimension.
• Embedding convex geometries and a bound on convex dimension
• The affine representation theorem for abstract convex geometries
• Comparing Dushnik-Miller dimension, Boolean dimension and local dimension
• Boolean dimension, components and blocks
• Greedoids
• Hyperplane arrangements with a lattice of regions
• The theory of convex geometries
• The convexity lattice of a poset
• Combinatorial representation and convex dimension of convex geometries
• Convexity in oriented matroids
• Cover-preserving order embeddings into Boolean lattices
• Embedding finite posets in cubes
• The fractional dimension of subsets of Boolean lattices and cartesian products
• On the fractional dimension of partially ordered sets
• Boolean dimension and local dimension
• Sparsity and dimension
• On difference graphs and the local dimension of posets
• Fractional local dimension
• Local dimension is unbounded for planar posets
• Combinatorics of lopsided sets
• Dimension and height for posets with planar cover graphs.
• Convexity in directed graphs
• Intransitive indifference with unequal indifference intervals
• Boolean dimension and tree-width
• Topological Minors of Cover Graphs and Dimension
• Partially ordered sets.

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