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Volumn 21, Issue 4, 2004, Pages 315-344

Lattice congruences of the weak order

Author keywords

Cambrian lattice; Congruence uniform; Coxeter group; Parabolic subgroup; Poset of regions; Shard; Simplicial hyperplane arrangement; Tamari lattice; Weak order

Indexed keywords


EID: 26244439459     PISSN: 01678094     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11083-005-4803-8     Document Type: Article
Times cited : (77)

References (25)
  • 1
    • 0000884168 scopus 로고
    • Orderings of Coxeter groups
    • (Boulder, Colo., 1983), Contemp. Math., Amer. Math. Soc., Providence, RI
    • 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.
    • (1984) Combinatorics and Algebra , vol.34 , pp. 175-195
    • Björner, A.1
  • 2
    • 0013012586 scopus 로고
    • Hyperplane arrangements with a lattice of regions
    • Björner, A., Edelman, P. and Ziegler, G.: Hyperplane arrangements with a lattice of regions, Discrete Comput. Geom. 5 (1990), 263-288.
    • (1990) Discrete Comput. Geom. , vol.5 , pp. 263-288
    • Björner, A.1    Edelman, P.2    Ziegler, G.3
  • 3
    • 0040494570 scopus 로고    scopus 로고
    • Shellable nonpure complexes and posets. II
    • Björner, A. and Wachs, M.: Shellable nonpure complexes and posets. II, Trans. Amer. Math. Soc. 349(10) (1997), 3945-3975.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , Issue.10 , pp. 3945-3975
    • Björner, A.1    Wachs, M.2
  • 5
    • 0141549792 scopus 로고    scopus 로고
    • Congruences in ordered sets
    • Chajda, I. and Snášel, V.: Congruences in ordered sets, Math. Bohem. 123(1) (1998), 95-100.
    • (1998) Math. Bohem. , vol.123 , Issue.1 , pp. 95-100
    • Chajda, I.1    Snášel, V.2
  • 6
    • 0141438237 scopus 로고
    • Congruence normality: The characterization of the doubling class of convex sets
    • Day, A.: Congruence normality: the characterization of the doubling class of convex sets, Algebra Universalis 31(3) (1994), 397-406.
    • (1994) Algebra Universalis , vol.31 , Issue.3 , pp. 397-406
    • Day, A.1
  • 7
    • 84967712844 scopus 로고
    • n dissected by hyperplanes
    • n dissected by hyperplanes, Trans. Amer. Math. Soc. 283(2) (1984), 617-631.
    • (1984) Trans. Amer. Math. Soc. , vol.283 , Issue.2 , pp. 617-631
    • Edelman, P.1
  • 8
    • 0347188734 scopus 로고    scopus 로고
    • Y-systems and generalized associahedra
    • Fomin, S. and Zelevinsky, A.: Y-systems and generalized associahedra, Ann. of Math. (2) 158(3) (2003), 977-1018.
    • (2003) Ann. of Math. (2) , vol.158 , Issue.3 , pp. 977-1018
    • Fomin, S.1    Zelevinsky, A.2
  • 9
    • 26244449488 scopus 로고
    • Math. Surveys Monographs, Amer. Math. Soc.
    • Freese, R., Ježek, J. and Nation, J.: Free Lattices, Math. Surveys Monographs 42, Amer. Math. Soc., 1995.
    • (1995) Free Lattices , vol.42
    • Freese, R.1    Ježek, J.2    Nation, J.3
  • 10
    • 0012535572 scopus 로고
    • On the distributivity of a lattice of lattice-congruences
    • Funayama, N. and Nakayama, T.: On the distributivity of a lattice of lattice-congruences, Proc. Imp. Acad. Tokyo 18 (1942), 553-554.
    • (1942) Proc. Imp. Acad. Tokyo , vol.18 , pp. 553-554
    • Funayama, N.1    Nakayama, T.2
  • 11
    • 0011030435 scopus 로고
    • On Tamari lattices
    • Geyer, W.: On Tamari lattices, Discrete Math. 133(1-3) (1994), 99-122.
    • (1994) Discrete Math. , vol.133 , Issue.1-3 , pp. 99-122
    • Geyer, W.1
  • 13
    • 0003950889 scopus 로고
    • Cambridge Studies in Advanced Mathematics, Cambridge Univ. Press
    • Humphreys, J.: Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge Univ. Press, 1990.
    • (1990) Reflection Groups and Coxeter Groups , vol.29
    • Humphreys, J.1
  • 15
    • 0000721182 scopus 로고
    • Duality between quasi-symmetric functions and the Solomon descent algebra
    • Malvenuto, C. and Reutenauer, C.: Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177(3) (1995), 967-982.
    • (1995) J. Algebra , vol.177 , Issue.3 , pp. 967-982
    • Malvenuto, C.1    Reutenauer, C.2
  • 16
    • 0003512464 scopus 로고
    • Grundlehren Math. Wiss., Springer-Verlag, Berlin
    • Orlik, P. and Terao, H.: Arrangements of Hyperplanes, Grundlehren Math. Wiss. 300, Springer-Verlag, Berlin, 1992.
    • (1992) Arrangements of Hyperplanes , vol.300
    • Orlik, P.1    Terao, H.2
  • 17
    • 0141465264 scopus 로고    scopus 로고
    • Order dimension, strong Bruhat order and lattice properties for posets
    • Reading, N.: Order dimension, strong Bruhat order and lattice properties for posets, Order 19(1) (2002), 73-100.
    • (2002) Order , vol.19 , Issue.1 , pp. 73-100
    • Reading, N.1
  • 18
    • 1542508681 scopus 로고    scopus 로고
    • Lattice and order properties of the poset of regions in a hyperplane arrangement
    • Reading, N.: Lattice and order properties of the poset of regions in a hyperplane arrangement, Algebra Universalis 50(2) (2003), 179-205.
    • (2003) Algebra Universalis , vol.50 , Issue.2 , pp. 179-205
    • Reading, N.1
  • 19
    • 0347534178 scopus 로고    scopus 로고
    • The order dimension of the poset of regions in a hyperplane arrangement
    • Reading, N.: The order dimension of the poset of regions in a hyperplane arrangement, J. Combin. Theory Ser. A 104(2) (2003), 265-285.
    • (2003) J. Combin. Theory Ser. A , vol.104 , Issue.2 , pp. 265-285
    • Reading, N.1
  • 20
    • 18144379891 scopus 로고    scopus 로고
    • Lattice congruences, fans and Hopf algebras
    • Reading, N.: Lattice congruences, fans and Hopf algebras, J. Combin. Theory Ser. A 110(2) (2005), 237-273.
    • (2005) J. Combin. Theory Ser. A , vol.110 , Issue.2 , pp. 237-273
    • Reading, N.1
  • 21
    • 33747165281 scopus 로고    scopus 로고
    • Cambrian lattices
    • to appear
    • Reading, N.: Cambrian lattices, Adv. Math., to appear.
    • Adv. Math.
    • Reading, N.1
  • 25
    • 31244433179 scopus 로고    scopus 로고
    • The patterns of permutations
    • Kleitman and Combinatorics: A Celebration
    • Wilf, H.: The patterns of permutations, in: Kleitman and Combinatorics: A Celebration, Discrete Math. 257(2-3) (2002), 575-583.
    • (2002) Discrete Math. , vol.257 , Issue.2-3 , pp. 575-583
    • Wilf, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.