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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