Lower bound cluster algebras: presentations, Cohen–Macaulayness, and normality
Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 95-114.

We give an explicit presentation for each lower bound cluster algebra. Using this presentation, we show that each lower bound algebra Gröbner degenerates to the Stanley–Reisner scheme of a vertex-decomposable ball or sphere, and is thus Cohen–Macaulay. Finally, we use Stanley–Reisner combinatorics and a result of Knutson–Lam–Speyer to show that all lower bound algebras are normal.

Received: 2017-08-02
Accepted: 2017-08-18
Published online: 2018-01-29
DOI: https://doi.org/10.5802/alco.2
Classification: 13F60,  05E40,  13F55
Keywords: Cluster algebras, lower bound cluster algebras, combinatorial commutative algebra, Stanley–Reisner complexes
@article{ALCO_2018__1_1_95_0,
     author = {Muller, Greg and Rajchgot, Jenna and Zykoski, Bradley},
     title = {Lower bound cluster algebras: presentations, Cohen--Macaulayness, and normality},
     journal = {Algebraic Combinatorics},
     pages = {95--114},
     publisher = {MathOA foundation},
     volume = {1},
     number = {1},
     year = {2018},
     doi = {10.5802/alco.2},
     zbl = {06882336},
     mrnumber = {3857161},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2018__1_1_95_0/}
}
Muller, Greg; Rajchgot, Jenna; Zykoski, Bradley. Lower bound cluster algebras: presentations, Cohen–Macaulayness, and normality. Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 95-114. doi : 10.5802/alco.2. https://alco.centre-mersenne.org/item/ALCO_2018__1_1_95_0/

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