ALGEBRAIC COMBINATORICS

no. 4

Towards a uniform subword complex description of acyclic finite type cluster algebras
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: 2017-12-20
Accepted: 2018-06-12
Published online: 2018-09-10
DOI: https://doi.org/10.5802/alco.25
Keywords: cluster algebra, F-polynomial, subword complexes 
@article{ALCO_2018__1_4_545_0,
     author = {Brodsky, Sarah B. and Stump, Christian},
     title = {Towards a uniform subword complex description of acyclic finite type cluster algebras},
     journal = {Algebraic Combinatorics},
     pages = {545--572},
     publisher = {MathOA foundation},
     volume = {1},
     number = {4},
     year = {2018},
     doi = {10.5802/alco.25},
     mrnumber = {3875076},
     zbl = {06963904},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2018__1_4_545_0/}
}
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/item/ALCO_2018__1_4_545_0/

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