Representations for the largest Extension of a closure system
Abstract
We consider extension of a closure system on a finite set S as a closure system on the same set S containing the given one as a sublattice. A closure system can be represented in different ways, e.g. by an implicational base or by the set of its meet-irreducible elements. When a closure system is described by an implicational base, we provide a characterization of the implicational base for the largest extension. We also show that the largest extension can be handled by a small modification of the implicational base of the input closure system. This answers a question asked in [12]. Second, we are interested in computing the largest extension when the closure system is given by the set of all its meet-irreducible elements. We give an incremental polynomial time algorithm to compute the largest extension of a closure system, and left open if the number of meet-irreducible elements grows exponentially.
Cite
@article{arxiv.2002.07680,
title = {Representations for the largest Extension of a closure system},
author = {Karima Ennaoui and Khaled Maafa and Lhouari Nourine},
journal= {arXiv preprint arXiv:2002.07680},
year = {2020}
}
Comments
16pages