Convexity in graphs and hypergraphs
SIAM Journal on Algebraic and Discrete Methods
Matroids and antimatroids—a survey
Discrete Mathematics
Discrete Mathematics
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Using concept lattices to uncover causal dependencies in software
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
Information Sciences: an International Journal
Key roles of closed sets and minimal generators in concise representations of frequent patterns
Intelligent Data Analysis
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Because antimatroid closure spaces satisfy the anti-exchange axiom, it is easy to show that they are uniquely generated. That is, the minimal set of elements determining a closed set is unique. A prime example is a discrete convex geometry in Euclidean space where closed sets are uniquely generated by their extreme points. But, many of the geometries arising in computer science, e.g. the world wide web or rectilinear VLSI layouts are not uniquely generated. Nevertheless, these closure spaces still illustrate a number of fundamental antimatroid properties which we demonstrate in this paper. In particular, we examine both a pseudo-convexity operator and the Galois closure of formal concept analysis. In the latter case, we show how these principles can be used to automatically convert a formal concept lattice into a system of implications.