Séminaire Lotharingien de Combinatoire, 91B.98 (2024), 12 pp.
Matias von Bell and Cesar Ceballos
Framing Lattices and Flow Polytopes
Abstract.
We introduce the framing lattice of a framed graph, a new lattice whose Hasse diagram is the dual graph of a framed triangulation of a flow polytope.
We show that every framing lattice is an HH lattice, hence polygonal, semidistributive, and congruence uniform. We also study lattice congruences determined by simple operations called M-moves. Framing lattices provide a unifying framework for the study of many remarkable lattice structures, and several well known results about them are straight forward corollaries of our results.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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