Bibliography

[1]     C. Amiot, On the structure of triangulated category with finitely many indecomposables, 27 pages, arxiv:math/0612141v1 [math.CT].

[2]     I. Assem, T. Brüstle, and R. Schiffler, Cluster-tilted algebras and slices, 21 pages, arXiv:0707.0038v2 [math.RT].

[3]     ----, Cluster-tilted algebras as trivial extensions, 14 pages, arXiv:math/0601537 [math.RT].

[4]     ----, On the Galois coverings of a cluster-tilted algebra, 21 pages, arXiv:0709.0850v1 [math.RT].

[5]     I. Assem, T. Brüstle, R. Schiffler, and G. Todorov, Cluster categories and duplicated algebras, J. Algebra 305 (2006), no. 1, 548-561.

[6]     Ch. A. Athanasiadis, Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes, Bull. London Math. Soc. 36 (2004), no. 3, 294-302.

[7]     ----, On a refinement of the generalized Catalan numbers for Weyl groups, Trans. Amer. Math. Soc. 357 (2005), no. 1, 179-196 (electronic).

[8]     ----, On some enumerative aspects of generalized associahedra, European J. Combin. 28 (2007), no. 4, 1208-1215.

[9]     Ch. A. Athanasiadis, Th. Brady, J. McCammond, and C. Watt, $h$-vectors of generalized associahedra and noncrossing partitions, Int. Math. Res. Not. (2006), Art. ID 69705, 28.

[10]     Ch. A. Athanasiadis, Th. Brady, and C. Watt, Shellability of noncrossing partition lattices, Proc. Amer. Math. Soc. 135 (2007), no. 4, 939-949 (electronic).

[11]     Ch. A. Athanasiadis and E. Tzanaki, On the enumeration of positive cells in generalized cluster complexes and Catalan hyperplane arrangements, J. Algebraic Combin. 23 (2006), no. 4, 355-375.

[12]     M. Barot, Ch. Geiss, and A. Zelevinsky, Cluster algebras of finite type and positive symmetrizable matrices, J. London Math. Soc. (2) 73 (2006), no. 3, 545-564.

[13]     J. Bell and M. Skandera, Multicomplexes and polynomials with real zeros, Discrete Math. 307 (2007), no. 6, 668-682.

[14]     A. Berenstein, S. Fomin, and A. Zelevinsky, Cluster algebras. III. Upper bounds and double Bruhat cells, Duke Math. J. 126 (2005), no. 1, 1-52.

[15]     A. Berenstein and A. Zelevinsky, Quantum cluster algebras, Adv. Math. 195 (2005), no. 2, 405-455.

[16]     N. Bergeron, Ch. Hohlweg, Lange C., and H. Thomas, Isometry classes of generalized associahedra, 12 pages, arXiv:0709.4421 [math.CO].

[17]     D. Bessis, The dual braid monoid, Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 5, 647-683.

[18]     D. Bessis and R. Corran, Non-crossing partitions of type $(e,e,r)$, Adv. Math. 202 (2006), no. 1, 1-49.

[19]     T. Bridgeland, Stability conditions on triangulated categories, 29 pages, to appear Annals of Math., math/0212237v3 [math.AG].

[20]     K. A. Brown, K. R. Goodearl, and M. Yakimov, Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space, Adv. Math. 206 (2006), no. 2, 567-629.

[21]     A. Buan, O. Iyama, I. Reiten, and J. Scott, Cluster structures for 2-Calabi-Yau categories and unipotent groups, 73 pages, arXiv:math/0701557v2 [math.RT].

[22]     A. Buan, R. Marsh, M. Reineke, I. Reiten, and G. Todorov, Tilting theory and cluster combinatorics, Adv. Math. 204 (2006), no. 2, 572-618.

[23]     A. Buan, R. Marsh, and I. Reiten, Cluster mutation via quiver representations, 28 pages, arXiv:math/0412077v2 [math.RT].

[24]     ----, Cluster-tilted algebras of finite representation type, J. Algebra 306 (2006), no. 2, 412-431.

[25]     ----, Cluster-tilted algebras, Trans. Amer. Math. Soc. 359 (2007), no. 1, 323-332 (electronic).

[26]     A. Buan, R. Marsh, I. Reiten, and G. Todorov, Clusters and seeds in acyclic cluster algebras, 12 pages, with an appendix coauthored in addition by P. Caldero and B. Keller, arXiv:math/0510359v3 [math.RT].

[27]     A. Buan and I. Reiten, Cluster algebras associated with extended dynkin quivers, 6 pages, arXiv:math/0507113v1 [marth.RT].

[28]     ----, From tilted to cluster-tilted algebras of dynkin type, 9 pages, arXiv:math/0510445v1 [math.RT].

[29]     ----, Acyclic quivers of finite mutation type, Int. Math. Res. Not. (2006), Art. ID 12804, 10.

[30]     A. Buan, I. Reiten, and A. Seven, Tame concealed algebras and cluster quivers of minimal infinite type, 16 pages, arXiv:math/0512137v2 [math.RT].

[31]     P. Caldero and B. Keller, From triangulated categories to cluster algebras, 31 pages, to appear Inventiones Math., arXiv:math/0506018v2.

[32]     P. Caldero and M. Reineke, On the quiver Grassmannian in the acyclic case, 16 pages, arXiv:math/0611074v2 [math.RT].

[33]     P. Caldero and A. Zelevinsky, Laurent expansions in cluster algebras via quiver representations, Mosc. Math. J. 6 (2006), no. 3, 411-429.

[34]     M.P. Carr and S.L. Devadoss, Coxeter complexes and graph-associahedra, Topology Appl. 153 (2006), no. 12, 2155-2168.

[35]     G. D. Carroll and D. Speyer, The cube recurrence, Electron. J. Combin. 11 (2004), no. 1, Research Paper 73, 31 pp. (electronic).

[36]     F. Chapoton, Enumerative properties of generalized associahedra, 15 pages, arXiv:math/0401237v1 [math.CO].

[37]     ----, Enumerative properties of generalized associahedra, Sém. Lothar. Combin. 51 (2004/05), Art. B51b, 16 pp. (electronic).

[38]     ----, Functional identities for the Rogers dilogarithm associated to cluster $Y$-systems, Bull. London Math. Soc. 37 (2005), no. 5, 755-760.

[39]     ----, Une base symétrique de l'algèbre des coinvariants quasi-symétriques, Electron. J. Combin. 12 (2005), Note 16, 7 pp. (electronic).

[40]     F. Chapoton, S. Fomin, and A. Zelevinsky, Polytopal realizations of generalized associahedra, Canad. Math. Bull. 45 (2002), no. 4, 537-566, Dedicated to Robert V. Moody.

[41]     L. O. Chekhov and V. V. Fock, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999), no. 3, 511-528, arXiv: math/9908165 [math.QA].

[42]     Suhyoung Choi and W. Goldman, The deformation spaces of convex $\Bbb{RP}\sp 2$-structures on 2-orbifolds, Amer. J. Math. 127 (2005), no. 5, 1019-1102.

[43]     R. Dehy and B. Keller, Index and h-vector, 10 pages, arXiv:0709.0882v1 [math.RT].

[44]     H. Derksen, J. Weyman, and A. Zelevinsky, Quivers with potentials and their representations I: Mutations, 58 pages, arXiv:0704.0649v3 [math.RA].

[45]     B. Drake, S. Gerrish, and M. Skandera, Two new criteria for comparison in the Bruhat order, Electron. J. Combin. 11 (2004), no. 1, Note 6, 4 pp. (electronic).

[46]     ----, Monomial nonnegativity and the Bruhat order, Electron. J. Combin. 11 (2004/06), no. 2, Research Paper 18, 5 pp. (electronic).

[47]     V. Fock and A Goncharov, Cluster ensembles, quantization and the dilogarithm, arXiv:math/0311245 [math.AG].

[48]     V. Fock and A. Goncharov, The quantum dilogarithm and representations quantized cluster varieties, 58 pages, arXiv: math/0702397v5 [math.QA].

[49]     ----, Cluster X-varieties, amalgamation and Poisson-Lie groups, Algebraic geometry and number theory,, Progr. Math., vol. 253, Birkhäuser Boston, Boston, MA, 2006, Volume dedicated to V. Drinfeld, pp. 27-68.

[50]     ----, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. (2006), no. 103, 1-211.

[51]     ----, Moduli spaces of convex projective structures on surfaces, Adv. Math. 208 (2007), no. 1, 249-273.

[52]     S. Fomin and N. Reading, Root systems and generalized associahedra, Lecture notes for IAS/Park-City 2004, 69 pages, arXiv:math.CO/0505518v2 [math.CO].

[53]     ----, Generalized cluster complexes and Coxeter combinatorics, Int. Math. Res. Not. (2005), no. 44, 2709-2757.

[54]     S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces. Part I: Cluster complexes., 56 pages, math.RA/0608367v3 [math.RA].

[55]     S. Fomin and A. Zelevinsky, Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2002), no. 2, 497-529 (electronic), arXiv:math/0104151v1 [math.RT].

[56]     ----, The Laurent phenomenon, Adv. in Appl. Math. 28 (2002), no. 2, 119-144.

[57]     ----, Cluster algebras. II. Finite type classification, Invent. Math. 154 (2003), no. 1, 63-121.

[58]     ----, $Y$-systems and generalized associahedra, Ann. of Math. (2) 158 (2003), no. 3, 977-1018.

[59]     ----, Cluster algebras. IV. Coefficients, Compos. Math. 143 (2007), no. 1, 112-164.

[60]     Ch. Fu and B. Keller, On cluster algebras with coefficients and 2-calabi-yau categories, 24 pages, arXiv:0710.3152v1 [math.RT].

[61]     Ch. Geiss, B. Leclerc, and J. Schröer, Auslander algebras and initial seeds for cluster algebras, 23 pages, to appear J. London Math. Soc., arXiv:math/0506405v4 [math.RT].

[62]     ----, Partial flag varieties and preprojective algebras, 42 pages, to appear in Annales de l'Institut Fourier, arXiv:math/0609138v3 [math.RT].

[63]     ----, Rigid modules over preprojective algebras II: The Kac-Moody case, 49 pages, arXiv:math/0703039v1 [math.RT].

[64]     ----, Semicanonical bases and preprojective algebras II: A multiplication formula, 22 pages, to appear in Compositio Math., arXiv:math/0509483v3 [math.RT].

[65]     ----, Semicanonical bases and preprojective algebras, Ann. Sci. École Norm. Sup. (4) 38 (2005), no. 2, 193-253.

[66]     ----, Rigid modules over preprojective algebras, Invent. Math. 165 (2006), no. 3, 589-632.

[67]     M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster algebras and Poisson geometry, Mosc. Math. J. 3 (2003), no. 3, 899-934, 1199, {Dedicated to Vladimir Igorevich Arnold on the occasion of his 65th birthday}.

[68]     ----, Cluster algebras and Weil-Petersson forms, Duke Math. J. 127 (2005), no. 2, 291-311.

[69]     W. Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990), no. 3, 791-845.

[70]     A. Goncharov, Pentagon relation for the quantum dilogarithm and quantized $\mathcal{M}^{\text{cyc}}_{0,5}$, to appear in Progress in Mathematics volume (Birkhauser) dedicated to the memory of Alexander Reznikov, arXiv/0704.405v2 [math.QA].

[71]     N. J. Hitchin, Lie groups and Teichmüller space, Topology 31 (1992), no. 3, 449-473.

[72]     Th. Holm and P. Jørgensen, Cluster categories and selfinjective algebras: type A, 18 pages, arXiv:math/0610728v1 [math.RT].

[73]     ----, Cluster categories and selfinjective algebras: type D, 21 pages, arXiv:math/0612451v1 [math.RT].

[74]     O. Iyama and I. Reiten, Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras, 53 pages, to appear in Amer. J. Math, arXiv:math/0605136v3 [math.RT].

[75]     R. M. Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998), no. 2, 105-115, arXiv:math/9706018 [math.QA].

[76]     B. Keller, On triangulated orbit categories, Doc. Math. 10 (2005), 551-581 (electronic).

[77]     B. Keller and I. Reiten, Acyclic calabi-yau categories, 16 pages, arXiv:math/0610594v2 [math.RT].

[78]     ----, Cluster-tilted algebras are Gorenstein and stably Calabi-Yau, Adv. Math. 211 (2007), no. 1, 123-151.

[79]     M. Kogan and A. Zelevinsky, On symplectic leaves and integrable systems in standard complex semisimple Poisson-Lie groups, Int. Math. Res. Not. (2002), no. 32, 1685-1702.

[80]     M. Kontsevich, Donaldson-thomas invariants, Notes for Mathematische Arbeitstagung, June 22-28 at MPIM Bonn, www.mpim-bonn.mpg.de/preprints/send?bid=3352.

[81]     C. Krattenthaler, The $M$-triangle of generalised non-crossing partitions for the types $E\sb 7$ and $E\sb 8$, Sém. Lothar. Combin. 54 (2005/06), Art. B541, 34 pp. (electronic).

[82]     Th. Lam and L. Williams, Total positivity for cominuscule Grassmannians, 39 pages, arXiv:0710.2932 [math.CO].

[83]     G. Lusztig, A survey of total positivity, 8 pages, arXiv:0705.3842v1 [math.RT].

[84]     ----, Total positivity in reductive groups, Lie theory and geometry, Progr. Math., vol. 123, Birkhäuser Boston, Boston, MA, 1994, pp. 531-568.

[85]     ----, Introduction to total positivity, Positivity in Lie theory: open problems, de Gruyter Exp. Math., vol. 26, de Gruyter, Berlin, 1998, pp. 133-145.

[86]     ----, Semicanonical bases arising from enveloping algebras, Adv. Math. 151 (2000), no. 2, 129-139.

[87]     R. Marsh, M. Reineke, and A. Zelevinsky, Generalized associahedra via quiver representations, Trans. Amer. Math. Soc. 355 (2003), no. 10, 4171-4186 (electronic).

[88]     J. McCammond, Noncrossing partitions in surprising locations, Amer. Math. Monthly 113 (2006), no. 7, 598-610.

[89]     G. Musiker and J. Propp, Combinatorial interpretations for rank-two cluster algebras of affine type, Electron. J. Combin. 14 (2007), no. 1, Research Paper 15, 23 pp. (electronic).

[90]     Y. Palu, Cluster characters for triangulated 2-Calabi-Yau categories, 21 pages, arXiv:math/0703540v2 [math.RT].

[91]     D. I. Panyushev, The poset of positive roots and its relatives, J. Algebraic Combin. 23 (2006), no. 1, 79-101.

[92]     R. C. Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987), no. 2, 299-339.

[93]     A. Postnikov, D. Speyer, and L. Williams, Matching polytopes, toric geometry, and the non-negative part of the grassmannian, 26 pages, arXiv:0706.2501 [math.AG].

[94]     N. Reading, Lattice congruences of the weak order, Order 21 (2004), no. 4, 315-344 (2005).

[95]     ----, Lattice congruences, fans and Hopf algebras, J. Combin. Theory Ser. A 110 (2005), no. 2, 237-273.

[96]     ----, Cambrian lattices, Adv. Math. 205 (2006), no. 2, 313-353.

[97]     V. Reiner and V. Welker, On the Charney-Davis and Neggers-Stanley conjectures, J. Combin. Theory Ser. A 109 (2005), no. 2, 247-280.

[98]     C.M. Ringel, The self-injective cluster tilted algebras, 5 pages, arXiv:0705.3903 [math.CO].

[99]     ----, some remarks concerning tilting modules and tilted algebras. origin. relevance. future., An appendix to the Handbook of Tilting Theory, arXiv:math/0605712 [math.RT].

[100]     N. Sandman, A type-B Tamari poset, Discrete Appl. Math. 143 (2004), no. 1-3, 110-122.

[101]     A. I. Seven, Recognizing cluster algebras of finite type, Electron. J. Combin. 14 (2007), no. 1, Research Paper 3, 35 pp. (electronic), arXiv:math/0406545v2 [math.CO].

[102]     R. Simion, A type-B associahedron, Adv. in Appl. Math. 30 (2003), no. 1-2, 2-25, Formal power series and algebraic combinatorics (Scottsdale, AZ, 2001).

[103]     D. Speyer and L. Williams, The tropical totally positive Grassmannian, J. Algebraic Combin. 22 (2005), no. 2, 189-210.

[104]     D. E. Speyer, Perfect matchings and the octahedron recurrence, J. Algebraic Combin. 25 (2007), no. 3, 309-348.

[105]     G. Tabuada, On the structure of Calabi-Yau categories with a cluster tilting subcategory, Doc. Math. 12 (2007), 193-213 (electronic).

[106]     J. Teschner, On the relation between quantum Liouville theory and the quantized Teichmüller spaces, Proceedings of 6th International Workshop on Conformal Field Theory and Integrable Models, vol. 19, 2004, pp. 459-477.

[107]     H. Thomas, Tamari lattices and noncrossing partitions in type $B$, Discrete Math. 306 (2006), no. 21, 2711-2723.

[108]     W. Thurston, The geometry and topology of three-manifolds, Princeton University notes, http://www.msri.org/publications/books/gt3m.

[109]     E. Tzanaki, Polygon dissections and some generalizations of cluster complexes, J. Combin. Theory Ser. A 113 (2006), no. 6, 1189-1198.

[110]     B. Webster and M. Yakimov, A Deodhar type stratification on the double flag variety, 21 pages, arXiv:math/0607374 [math.SG].

[111]     L. Williams, Shelling totally nonnegative flag varieties, 21 pages, math.RT/0509129 [math.RT].

[112]     A. Zelevinsky, Nested complexes and their polyhedral realizations, Pure Appl. Math. Q. 2 (2006), no. 3, 655-671, arXiv:math/0507277 [math.CO].

[113]     Bin Zhu, Generalized cluster complexes via quiver representations, 20 pages, to appear J. Algebraic Comb., arXiv:math/0607155v5 [math.RT].

[114]     ----, Preprojective cluster variables of acyclic cluster algebras, 18 pages, arXiv:math/0511706v3 [math.RT].

[115]     ----, Applications of BGP-reflection functors: isomorphisms for cluster algebras, Sci. China Ser. A 49 (2006), no. 12, 1839-1854.

[116]     ----, Equivalences between cluster categories, J. Algebra 304 (2006), no. 2, 832-850.

[117]     ----, BGP-reflection functors and cluster combinatorics, J. Pure Appl. Algebra 209 (2007), no. 2, 497-506.