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arXiv · 1301.0759

Pruning a poset with veins

Paul Poncet
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Abstract

We recall some abstract connectivity concepts, and apply them to special chains in partially ordered sets, called veins, that are defined as order-convex chains that are contained in every maximal chain they meet. Veins enable us to define a new partial order on the same underlying set, called the pruning order. The associated pruned poset is simpler than the initial poset, but irreducible, coirreducible, and doubly-irreducible elements are preserved by the operation of pruning.

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Paul Poncet. 2013-01-04. Pruning a poset with veins. https://arxiv.org/abs/1301.0759

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