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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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