Minkowski decompositions for generalized associahedra of acyclic type

Autor:	Christian Stump, Robert Löwe, Dennis Jahn
Rok vydání:	2021
Předmět:	Initial Seed Polytope Type (model theory) Cluster algebra Combinatorics Cone (topology) Minkowski space FOS: Mathematics Cluster (physics) Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Variety (universal algebra) Mathematics
Zdroj:	Algebraic Combinatorics. 4:757-775
ISSN:	2589-5486
DOI:	10.5802/alco.177
Popis:	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. 17 pages. v2: updated and extended examples, added footnote that Theorem 1.4 also follows from [AHL20, Theorems 4.1 & 4.2]
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb2b5bc869ed29ceecbba59e49cb56ff https://doi.org/10.5802/alco.177 Zobrazit plný text záznamu