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2018•arXiv (Cornell University)Open access

Polytopes of independent sets of relations and their 1-skeleta

Farid Aliniaeifard, Carolina Benedetti, Nantel Bergeron, Shu Xiao Li, Franco Saliola

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Abstract

We characterize the edges of two classes of $0/1$-polytopes whose vertices encode the of a relation on a finite set. The first class includes poset chain polytopes, the vertex packing polytopes from graph theory, some instances of matroid independence polytopes, as well as newly-defined polytopes whose vertices correspond to noncrossing set partitions. In analogy with matroid basis polytopes, the second class is obtained by considering the independent sets of maximal cardinality.

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What this paper is about

We characterize the edges of two classes of $0/1$-polytopes whose vertices encode the of a relation on a finite set. The first class includes poset chain polytopes, the vertex packing polytopes from graph theory, some instances of matroid independence polytopes, as well as newly-defined polytopes whose vertices correspond to noncrossing set partitions. In analogy with matroid basis polytopes, the second class is obtained by considering the independent sets of maximal cardinality.

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Available abstract

We characterize the edges of two classes of $0/1$-polytopes whose vertices encode the of a relation on a finite set. The first class includes poset chain polytopes, the vertex packing polytopes from graph theory, some instances of matroid independence polytopes, as well as newly-defined polytopes whose vertices correspond to noncrossing set partitions. In analogy with matroid basis polytopes, the second class is obtained by considering the independent sets of maximal cardinality.

Key concepts: Matroid, Polytope, Combinatorics, Mathematics, Partially ordered set, Vertex (graph theory), Independent set, Class (philosophy)

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