Lattice Congruences of the Weak Order

Björner, A.: Orderings of Coxeter groups, in: Combinatorics and Algebra (Boulder, Colo., 1983), Contemp. Math. 34, Amer. Math. Soc., Providence, RI, 1984, pp. 175–195.

Björner, A., Edelman, P. and Ziegler, G.: Hyperplane arrangements with a lattice of regions, Discrete Comput. Geom. 5 (1990), 263–288.

Björner, A. and Wachs, M.: Shellable nonpure complexes and posets. II, Trans. Amer. Math. Soc. 349(10) (1997), 3945–3975.

Caspard, N., Le Conte de Poly-Barbut, C. and Morvan, M.: Cayley lattices of finite Coxeter groups are bounded, Adv. in Appl. Math. 33(1) (2004), 71–94.

Chajda, I. and Snášel, V.: Congruences in ordered sets, Math. Bohem. 123(1) (1998), 95–100.

Day, A.: Congruence normality: the characterization of the doubling class of convex sets, Algebra Universalis 31(3) (1994), 397–406.

Edelman, P.: A partial order on the regions of ℝn dissected by hyperplanes, Trans. Amer. Math. Soc. 283(2) (1984), 617–631.

Fomin, S. and Zelevinsky, A.: Y-systems and generalized associahedra, Ann. of Math. (2) 158(3) (2003), 977–1018.

Freese, R., Ježek, J. and Nation, J.: Free Lattices, Math. Surveys Monographs 42, Amer. Math. Soc., 1995.

Funayama, N. and Nakayama, T.: On the distributivity of a lattice of lattice-congruences, Proc. Imp. Acad. Tokyo 18 (1942), 553–554.

Geyer, W.: On Tamari lattices, Discrete Math. 133(1–3) (1994), 99–122.

Grätzer, G.: General Lattice Theory, 2nd edn, Birkhäuser Verlag, Basel, 1998.

Humphreys, J.: Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge Univ. Press, 1990.

Jedlička, P.: A combinatorial construction of the weak order of a Coxeter group, Preprint, 2003.

Malvenuto, C. and Reutenauer, C.: Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177(3) (1995), 967–982.

Orlik, P. and Terao, H.: Arrangements of Hyperplanes, Grundlehren Math. Wiss. 300, Springer-Verlag, Berlin, 1992.

Reading, N.: Order dimension, strong Bruhat order and lattice properties for posets, Order 19(1) (2002), 73–100.

Reading, N.: Lattice and order properties of the poset of regions in a hyperplane arrangement, Algebra Universalis 50(2) (2003), 179–205.

Reading, N.: The order dimension of the poset of regions in a hyperplane arrangement, J. Combin. Theory Ser. A 104(2) (2003), 265–285.

Reading, N.: Lattice congruences, fans and Hopf algebras, J. Combin. Theory Ser. A 110(2) (2005), 237–273.

Reading, N.: Cambrian lattices, Adv. Math., to appear.

Sloane, N. J. A. (ed.): The On-Line Encyclopedia of Integer Sequences, published electronically at http://www.research.att.com/~njas/sequences/, 2003.

Stembridge, J.: A Maple package for posets, available electronically at http://www.math.lsa.umich.edu/~jrs/maple.html.

Thomas, H.: Tamari lattices for types B and D, Preprint math.CO/0311334, 2003.

Wilf, H.: The patterns of permutations, in: Kleitman and Combinatorics: A Celebration, Discrete Math. 257(2–3) (2002), 575–583.