Title: Wilting Theory of Flow Polytopes

Abstract: Given a framed directed acyclic graph (DAG), we consider the DKK graph whose vertices are the maximal cliques of pairwise coherent routes and whose edges connect cliques which differ by only one route. Given a set of edges marked as “wilted,” we study the maximal cliques which avoid all wilted arrows. We define a class of framed DAGs whose DKK graphs may be realized as intervals in the DKK lattice of an amply framed DAG and we obtain interesting decompositions of the DKK graph of a general framed DAG. In particular, we may realize decompositions of the Tamari lattice into nu-Tamari intervals in this way.