Convex geometries

Kira Adaricheva, J. B. Nation

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Citations (Scopus)

Abstract

The origin of convex geometries lies in combinatorics, and the goal of the study of finite convex geometries was to develop the combinatorial abstraction of convexity. Similarly, the theory of matroids is a combinatorial abstraction of independent sets; see the survey of B. Dietrich [125]. Since both abstractions can be formulated in the framework of a closure operator on a finite set, one can associate with a convex geometry or a matroid the closure lattice of the corresponding closure operator. This also becomes the foundation for the generalization of these concepts to the infinite case.

Original languageEnglish
Title of host publicationLattice Theory
Subtitle of host publicationSpecial Topics and Applications
PublisherSpringer International Publishing
Pages153-179
Number of pages27
Volume2
ISBN (Electronic)9783319442365
ISBN (Print)9783319442358
DOIs
Publication statusPublished - Jan 1 2016

Fingerprint

Convex Geometry
Closure Operator
Matroid
Finite Geometry
Independent Set
Combinatorics
Convexity
Finite Set
Closure
Abstraction

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Adaricheva, K., & Nation, J. B. (2016). Convex geometries. In Lattice Theory: Special Topics and Applications (Vol. 2, pp. 153-179). Springer International Publishing. https://doi.org/10.1007/978-3-319-44236-5_5

Convex geometries. / Adaricheva, Kira; Nation, J. B.

Lattice Theory: Special Topics and Applications. Vol. 2 Springer International Publishing, 2016. p. 153-179.

Research output: Chapter in Book/Report/Conference proceedingChapter

Adaricheva, K & Nation, JB 2016, Convex geometries. in Lattice Theory: Special Topics and Applications. vol. 2, Springer International Publishing, pp. 153-179. https://doi.org/10.1007/978-3-319-44236-5_5
Adaricheva K, Nation JB. Convex geometries. In Lattice Theory: Special Topics and Applications. Vol. 2. Springer International Publishing. 2016. p. 153-179 https://doi.org/10.1007/978-3-319-44236-5_5
Adaricheva, Kira ; Nation, J. B. / Convex geometries. Lattice Theory: Special Topics and Applications. Vol. 2 Springer International Publishing, 2016. pp. 153-179
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