Compatibility fans for graphical nested complexes

Vincent Pilaud
CNRS \& LIX, \'Ecole Polytechnique

Thibault Manneville
LIX, \'Ecole Polytechnique



Content: Generalizing the classical associahedron, M.~Carr and S.~Devadoss constructed graph associahedra which provide polytopal realizations of the nested complex of a graph $G$. This talk will present multiple alternative realizations of graphical nested complexes as complete simplicial fans, using ideas coming from compatibility degrees and cluster fans constructed by S.~Fomin and A.~Zelevinsky in their study of finite type cluster algebras. When the graph $G$ is a path, this construction recovers F.~Santos' Catalan many simplicial fan realizations of the associahedron. Preprint available at \texttt{arXiv:1501.07152}.

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