Minkowski decompositions for generalized associahedra of acyclic type
Combinatorics
2020-06-19 v2
Abstract
We give an explicit subword complex description of the generators of the type cone of the g-vector fan of a finite type cluster algebra with acyclic initial seed. This yields in particular a description of the Newton polytopes of the F-polynomials in terms of subword complexes as conjectured by S. Brodsky and the third author. We then show that the cluster complex is combinatorially isomorphic to the totally positive part of the tropicalization of the cluster variety as conjectured by D. Speyer and L. Williams.
Keywords
Cite
@article{arxiv.2005.14065,
title = {Minkowski decompositions for generalized associahedra of acyclic type},
author = {Dennis Jahn and Robert Löwe and Christian Stump},
journal= {arXiv preprint arXiv:2005.14065},
year = {2020}
}
Comments
17 pages. v2: updated and extended examples, added footnote that Theorem 1.4 also follows from [AHL20, Theorems 4.1 & 4.2]