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 - and -vectors, and by providing a conjectured description of the Newton polytopes of the -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 -polynomials or of the cluster variables, respectively. We prove this conjectured description to hold in type and in all types of rank at most including all exceptional types, leaving types , , and conjectural.
Accepted:
Published online:
DOI: 10.5802/alco.25
@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 = {http://archive.numdam.org/articles/10.5802/alco.25/} }
TY - JOUR AU - Brodsky, Sarah B. AU - Stump, Christian TI - Towards a uniform subword complex description of acyclic finite type cluster algebras JO - Algebraic Combinatorics PY - 2018 SP - 545 EP - 572 VL - 1 IS - 4 PB - MathOA foundation UR - http://archive.numdam.org/articles/10.5802/alco.25/ DO - 10.5802/alco.25 LA - en ID - ALCO_2018__1_4_545_0 ER -
%0 Journal Article %A Brodsky, Sarah B. %A Stump, Christian %T Towards a uniform subword complex description of acyclic finite type cluster algebras %J Algebraic Combinatorics %D 2018 %P 545-572 %V 1 %N 4 %I MathOA foundation %U http://archive.numdam.org/articles/10.5802/alco.25/ %R 10.5802/alco.25 %G en %F 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. http://archive.numdam.org/articles/10.5802/alco.25/
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