A geometric approach to acyclic orientations
Richard Ehrenborg, MLE Slone
TL;DR
This paper presents a geometric proof that the set of acyclic orientations with a fixed sink in a connected graph forms a poset decomposable into disjoint distributive lattices.
Contribution
It provides a geometric proof of Propp's result, revealing the lattice structure of acyclic orientations with a fixed sink.
Findings
The poset of acyclic orientations decomposes into distributive lattices.
The proof offers a geometric perspective on the structure of acyclic orientations.
This approach clarifies the combinatorial structure of orientations with a fixed sink.
Abstract
The set of acyclic orientations of a connected graph with a given sink has a natural poset structure. We give a geometric proof of a result of Jim Propp: this poset is the disjoint union of distributive lattices.
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