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@article{BFZup,
AUTHOR ={Berenstein, A. and Fomin, S. and Zelevinsky, A.}, 
 TITLE = {Cluster algebras III: Upper bounds and double Bruhat cells},
   JOURNAL = {Duke Math. J.},
   FJOURNAL = {Duke Mathematical Journal},
     VOLUME = {126},
         YEAR =  {2005}, 
           NUMBER={1},
      PAGES = {1--52},
  MRNUMBER = {2110627},
       DOI = {10.1215/S0012-7094-04-12611-9}
       }
 

@article{DWZ,
AUTHOR ={ Derksen, H. and Weyman,  J.  and  Zelevinsky, A.}, 
 TITLE = {Quivers with potentials and their representations II:
Applications to cluster algebras},
JOURNAL = {J. Amer. Math. Soc.},
 FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {23},
      YEAR = {2010},
    NUMBER = {3},
     PAGES = {497--608},
  MRNUMBER = {2629987},
       DOI = {10.1090/S0894-0347-10-00662-4}
         }
 



%
@article{DKR,
AUTHOR ={D\'esarm\'enien, J. and  Kung, J.P.S. and  Rota, G.-C.}, 
 TITLE = {Invariant theory, Young bitableaux and Combinatorics},
   JOURNAL = { Adv. Math.},
   FJOURNAL = {Advances in Mathematics},
    VOLUME = {27},
      YEAR = {1978},
    NUMBER = {1},
     PAGES = {63--92},
  MRNUMBER = {0485944},
       DOI = {10.1016/0001-8708(78)90077-4}
        }
 

  

%
@article{FZ1,
AUTHOR ={ S.~Fomin and A.~Zelevinsky}, 
 TITLE = {Cluster Algebras. I.
 Foundations},
 JOURNAL = {J. Amer. Math. Soc.},
 FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {15},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {497--608},
   MRCLASS = {16S99 (14M99 17B99)},
  MRNUMBER = {1887642},
       DOI = {10.1090/S0894-0347-01-00385-X}
         }
 




%
@article{FZ4,
AUTHOR ={Fomin, S and Zelevinsky, A.}, 
 TITLE = {Cluster Algebras IV: Coefficients},
   JOURNAL = {Compos. Math.},
    FJOURNAL = {Compositio Mathematica},
     VOLUME = {143},
      YEAR =  {2007}, 
      NUMBER={1},
          PAGES = {112--164},
            MRCLASS = {16S99 (05E15 14M17 22E46)},
  MRNUMBER = {2295199},
       DOI = {10.1112/S0010437X06002521}
       }



%
@article{Fulton,
AUTHOR = {Fulton, W.},
     TITLE = {Young tableaux},
    SERIES = {London Mathematical Society Student Texts},
    VOLUME = {35},
      NOTE = {With applications to representation theory and geometry},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {x+260},
   MRCLASS = {05E10 (05E05 05E15 14M15 20G05)},
  MRNUMBER = {1464693},
MRREVIEWER = {Tadeusz J\'{o}zefiak}}
%

@article {GHKK,
    AUTHOR = {Gross, M. and Hacking, P. and Keel, S. and Kontsevich,
              M.},
     TITLE = {Canonical bases for cluster algebras},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {31},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {497--608},
   MRCLASS = {13F60 (14J33)},
  MRNUMBER = {3758151},
       DOI = {10.1090/jams/890}
       }
       



@article{Keller,
AUTHOR ={Irelli, G.-C. and   Keller, B. and  Labardini-Fragoso, D. and  Plamondon, P.-G.}, 
 TITLE = { Linear independence of cluster monomials for skew-symmetric cluster algebras},
JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {149},
      YEAR = {2013},
    NUMBER = {10},
     PAGES = {1753--1764},
   MRCLASS = {13F60 (18E30)},
  MRNUMBER = {3123308},
       DOI = {10.1112/S0010437X1300732X}
       }
       
@misc{K14,
AUTHOR ={Koshevoy, G.}, 
 Eprint = {1411.3569},
 Eprinttype = {arxiv},
 TITLE = {Cluster monomials in $C[GL_n/N]$, a simplicial fan in the cone of semi-standard Young tableaux, and the Lusztig basis},
 Year = {2014}}

@misc{Magee,
AUTHOR ={Magee, T.}, 
 TITLE = {Fock-Goncharov conjecture and polyhedral cones for $U\subset SL_n$ and base affine space $SL_n/U$},
  Eprint = {1502.03769},
  Eprinttype = {arxiv},
  Year = {2015}}
 
 
 @article{pos,
AUTHOR ={ K.~ Lee and R.~ Schiffler}, 
 TITLE = { Positivity for cluster algebras},
 JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series },
    VOLUME = {182},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {73--125},
  MRNUMBER = {MR3374957},
       DOI = {10.4007/annals.2015.182.1.2}
       }
       

 @article{L,
AUTHOR ={ G.~Lusztig}, 
 TITLE = {Canonical bases arising from quantized enveloping algebras},
   FJOURNAL = {J. Amer. Math. Soc.},
     VOLUME = {3},
      YEAR =  {1990}, 
      PAGES = {447--498}}

 @article{MS,
 AUTHOR = {Miller, E. and Sturmfels, B.},
     TITLE = {Combinatorial commutative algebra},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {227},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2005},
     PAGES = {xiv+417},
   MRCLASS = {13-01 (05-01 05E99 13D02 14M15 14M25)},
  MRNUMBER = {2110098},
MRREVIEWER = {Joseph Gubeladze}
  }