ALGEBRAIC COMBINATORICS

no. 4
Towards a uniform subword complex description of acyclic finite type cluster algebras
Brodsky, Sarah B.1; Stump, Christian1
1 Institut für Mathematik, Technische Universität Berlin, Germany
Algebraic Combinatorics, Volume 1 (2018) no. 4, pp. 545-572.

It has been established in recent years how to approach acyclic cluster algebras of finite type using subword complexes. We continue this study by uniformly describing the c- and g-vectors, and by providing a conjectured description of the Newton polytopes of the F-polynomials. We moreover show that this conjectured description would imply that finite type cluster complexes are realized by the duals of the Minkowski sums of the Newton polytopes of either the F-polynomials or of the cluster variables, respectively. We prove this conjectured description to hold in type A and in all types of rank at most 8 including all exceptional types, leaving types B, C, and D conjectural.

Received:
Accepted:
Published online:
DOI: 10.5802/alco.25
Keywords: cluster algebra, $F$-polynomial, subword complexes
Brodsky, Sarah B. 1; Stump, Christian 1

1 Institut für Mathematik, Technische Universität Berlin, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Brodsky, Sarah B.; Stump, Christian. Towards a uniform subword complex description of acyclic finite type cluster algebras. Algebraic Combinatorics, Volume 1 (2018) no. 4, pp. 545-572. doi : 10.5802/alco.25. https://alco.centre-mersenne.org/articles/10.5802/alco.25/

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