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2003•Journal of Shaanxi Normal UniversityRequires access

Relations between poset matroids and greedoids

Liu San

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Abstract

This paper deals with the relations between poset matroids and greedoids. The first is to show that any poset matroid is a greedoid by comparing the property of rank closure operator of poset matroids with the relative property of closure operator of greedoids. In addition, by comparing the axioms of automorphism group of greedoids with that of poset matroids, it is proved that a greedoid is not necessary a poset matroid.

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What this paper is about

This paper deals with the relations between poset matroids and greedoids. The first is to show that any poset matroid is a greedoid by comparing the property of rank closure operator of poset matroids with the relative property of closure operator of greedoids. In addition, by comparing the axioms of automorphism group of greedoids with that of poset matroids, it is proved that a greedoid is not necessary a poset matroid.

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Available abstract

This paper deals with the relations between poset matroids and greedoids. The first is to show that any poset matroid is a greedoid by comparing the property of rank closure operator of poset matroids with the relative property of closure operator of greedoids. In addition, by comparing the axioms of automorphism group of greedoids with that of poset matroids, it is proved that a greedoid is not necessary a poset matroid.

Key concepts: Matroid, Partially ordered set, Graphic matroid, Combinatorics, Mathematics, Property (philosophy), Closure (psychology), Rank (graph theory)

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