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arXiv · 2002.07680

Representations for the largest Extension of a closure system

Karima Ennaoui·Khaled Maafa·Lhouari Nourine
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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.

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Karima Ennaoui, Khaled Maafa, Lhouari Nourine. 2020-02-18. Representations for the largest Extension of a closure system. https://arxiv.org/abs/2002.07680

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