Séminaire Lotharingien de Combinatoire, 84B.13 (2020), 12 pp.

Arnau Padrol, Yann Palu, Vincent Pilaud and Pierre-Guy Plamondon

On Type Cones of g-Vector Fans

Abstract. We study the type cone (i.e., the space of all polytopal realizations) of g-vector fans of finite type cluster-like complexes (finite type cluster complexes, non-kissing complexes of gentle algebra, and graphical nested complexes). We show that this cone is often simplicial, which explains an elegant "kinematic" construction of the associahedron as a section of a high dimensional positive orthant by certain affine subspaces parametrized by a low dimensional positive orthant.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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