# ALGEBRAIC COMBINATORICS

Minkowski decompositions for generalized associahedra of acyclic type
Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 757-775.

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.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.177
Classification: 13F60,  20F55,  52B05,  05E45
Keywords: Cluster algebras, F-polynomials, subword complex, type cone.
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author = {Jahn, Dennis and L\"owe, Robert and Stump, Christian},
title = {Minkowski decompositions for generalized associahedra of acyclic type},
journal = {Algebraic Combinatorics},
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volume = {4},
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year = {2021},
doi = {10.5802/alco.177},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.177/}
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Jahn, Dennis; Löwe, Robert; Stump, Christian. Minkowski decompositions for generalized associahedra of acyclic type. Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 757-775. doi : 10.5802/alco.177. https://alco.centre-mersenne.org/articles/10.5802/alco.177/

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