Séminaire Lotharingien de Combinatoire, 84B.65 (2020), 12 pp.

Hugh Thomas and Nathan Williams

Independence Posets

Abstract. Let G be an acyclic directed graph. For each vertex g in G, we define an involution on the independent sets of G. We call these involutions flips, and use them to define the independence poset for G - a new partial order on independent sets of G. Our independence posets are a generalization of distributive lattices, eliminating the lattice requirement: an independence poset that is a graded lattice is always a distributive lattice. Many well-known posets turn out to be special cases of our construction.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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