Cambrian lattices

Advances in Mathematics

Volumn 205, Issue 2, 2006, Pages 313-353

  Reading, Nathan ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Cluster; Coxeter group; Fiber polytope; Generalized associahedron; Lattice congruence; Lattice quotient; Tamari lattice

Indexed keywords

EID: 33747165281     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2005.07.010     Document Type: Article

References (34)

1. Billera L., and Sturmfels B. Fiber polytopes. Ann. Math. (2) 135 3 (1992) 527-549
2. Billera L., and Sturmfels B. Iterated fiber polytopes. Mathematika 41 2 (1994) 348-363
3. A. Björner, Orderings of Coxeter groups, Combinatorics and Algebra, Boulder, CO, 1983, pp. 175-195, Contemp. Math. 34, American Mathematical Society, Providence, RI, 1984.
4. Björner A., and Wachs M. Shellable nonpure complexes and posets. II. Trans. Amer. Math. Soc. 349 10 (1997) 3945-3975
5. Bott R., and Taubes C. On the self-linking of knots, Topology and Physics. J. Math. Phys. 35 10 (1994) 5247-5287
6. N. Bourbaki, Lie groups and Lie algebras, Chapters 4-6, Translated from the 1968 French original by Andrew Pressley, Elements of Mathematics, Springer, Berlin, 2002.
7. Caspard N., Le Conte de Poly-Barbut C., and Morvan M. Cayley lattices of finite Coxeter groups are bounded. Adv. Appl. Math. 33 1 (2004) 71-94
8. Chajda I., and Snášel V. Congruences in ordered sets. Math. Bohem. 123 1 (1998) 95-100
9. Chapoton F., Fomin S., and Zelevinsky A. Polytopal realizations of generalized associahedra. Canad. Math. Bull. 45 4 (2002) 537-566
10. Day A. Congruence normality: the characterization of the doubling class of convex sets. Algebra Universalis 31 3 (1994) 397-406
11. S. Fomin, N. Reading, Root systems and generalized associahedra, Lecture Notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics, math.CO/0505518, 2004.
12. Fomin S., and Zelevinsky A. Cluster algebras. II. Finite type classification. Invent. Math. 154 1 (2003) 63-121
13. Fomin S., and Zelevinsky A. Y-systems and generalized associahedra. Ann. Math. 158 (2003) 977-1018
14. R. Freese, J. Ježek, J. Nation, Free Lattices, Mathematical Surveys and Monographs, vol. 42, American Mathematical Society, 1995.
15. Funayama N., and Nakayama T. On the distributivity of a lattice of lattice-congruences. Proc. Imp. Acad. Tokyo 18 (1942) 553-554
16. Geyer W. On Tamari lattices. Discrete Math. 133 1-3 (1994) 99-122
17. Grätzer G. General lattice Theory. second ed. (1998), Birkhäuser, Basel
18. Humphreys J. Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics vol. 29 (1990), Cambridge University Press, Cambridge
19. Le Conte de Poly-Barbut C. Sur les Treillis de Coxeter Finis (French). Math. Inf. Sci. Hum. 32 125 (1994) 41-57
20. Loday J.-L. Realization of the Stasheff polytope. Arch. Math. 83 (2004) 267-278
21. Marsh R., Reineke M., and Zelevinsky A. Generalized associahedra via quiver representations. Trans. Amer. Math. Soc. 355 10 (2003) 4171-4186
22. Reading N. Order dimension, strong Bruhat order and lattice properties for posets. Order 19 1 (2002) 73-100
23. N. Reading, Lattice congruences of the weak order, Order, to appear.
24. Reading N. Lattice congruences, fans and Hopf algebras. J. Combin. Theory Ser. A 110 2 (2005) 237-273
25. N. Reading, Clusters, Coxeter-sortable elements and noncrossing partitions, math.CO/0507186, 2005.
26. N. Reading, Sortable elements and Cambrian lattices, in preparation.
27. Reiner V. Non-crossing partitions for classical reflection groups. Discrete Math. 177 1-3 (1997) 195-222
28. Reiner V. Equivariant fiber polytopes. Doc. Math. 7 (2002) 113-132 (electronic)
29. Simion R. Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations. Electron. J. Combin. 7 1 (2000) (Research Paper 9, 27pp.)
30. Simion R. A type-B associahedron, Formal power series and algebraic combinatorics, Scottsdale, AZ, 2001. Adv. Appl. Math. 30 1-2 (2003) 2-25
31. J. Stasheff, From operads to "physically" inspired theories, Operads: Proceedings of Renaissance Conferences, Hartford, CT/Luminy, 1995, pp. 53-81, Contemp. Math. 202 (1997).
32. H. Thomas, Tamari lattices for types B and D, math.CO/0311334, 2003.
33. Wilf H. The patterns of permutations, Kleitman and combinatorics: a celebration. Discrete Math. 257 2-3 (2002) 575-583
34. A. Zelevinsky, personal communication, 2004.