Representing finite convex geometries by relatively convex sets

Kira Adaricheva

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

A closure system with the anti-exchange axiom is called a convex geometry. One geometry is called a sub-geometry of the other if its closed sets form a sublattice in the lattice of closed sets of the other. We prove that convex geometries of relatively convex sets in n-dimensional vector space and their finite sub-geometries satisfy the n-Carousel Rule, which is the strengthening of the n-Carathéodory property. We also find another property, that is similar to the simplex partition property and independent of 2-Carousel Rule, which holds in sub-geometries of 2-dimensional geometries of relatively convex sets.

Original languageEnglish
Pages (from-to)68-78
Number of pages11
JournalEuropean Journal of Combinatorics
Volume37
DOIs
Publication statusPublished - Apr 2014

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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