메뉴 건너뛰기




Volumn 33, Issue 1, 2004, Pages 71-94

Cayley lattices of finite Coxeter groups are bounded

Author keywords

Bounded lattice; Coxeter group and lattice; Doubling operation; Reflection; Semidistributivity; Zonotope

Indexed keywords


EID: 3142738728     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aam.2003.09.002     Document Type: Article
Times cited : (31)

References (21)
  • 1
    • 0003756662 scopus 로고
    • Ordre et classification
    • Paris, France: Hachette
    • Barbut M. Monjardet B. Ordre et classification vols. 1 and 2 1970 Hachette Paris, France
    • (1970) , vol.1-2
    • Barbut, M.1    Monjardet, B.2
  • 2
    • 0003289716 scopus 로고
    • Lattice Theory
    • ed. Providence, RI
    • Birkhoff G. Lattice Theory, 1st ed. 1940 Amer. Math. Soc. Providence, RI
    • (1940) Amer. Math. Soc. , Issue.1
    • Birkhoff, G.1
  • 3
    • 0000884168 scopus 로고
    • Orderings of Coxeter groups
    • Contemp. Math., Providence, RI: Amer. Math. Soc
    • Björner A. Orderings of Coxeter groups Contemp. Math. vol. 34 1984 175-195 Amer. Math. Soc. Providence, RI
    • (1984) Amer. Math. Soc. , vol.34 , pp. 175-195
    • Björner, A.1
  • 5
    • 0004115280 scopus 로고
    • Groupes et Algèbres de Lie
    • Chapitres 4, 5, 6 Paris: Hermann
    • Bourbaki N. Groupes et Algèbres de Lie, Chapitres 4, 5, 6 Éléments de Mathématiques vol. 34 1968 Hermann Paris
    • (1968) Éléments de Mathématiques , vol.34
    • Bourbaki, N.1
  • 6
    • 0347368290 scopus 로고    scopus 로고
    • The lattice of permutations is bounded
    • Caspard N. The lattice of permutations is bounded Internat. J. Algebra Comput. 10 4 2000 481-489
    • (2000) Internat. J. Algebra Comput. , vol.10 , Issue.4 , pp. 481-489
    • Caspard, N.1
  • 7
    • 3142750760 scopus 로고    scopus 로고
    • Tamari lattices are bounded: A new proof
    • Preprint
    • N. Caspard, C. Le Conte de Poly-Barbut, Tamari lattices are bounded: a new proof, Preprint, 2003
    • (2003)
    • Caspard, N.1    Le Conte de Poly-Barbut, C.2
  • 8
    • 3142743410 scopus 로고    scopus 로고
    • Lines arrangements of reflections in Coxeter groups
    • Preprint
    • N. Caspard, H. Crapo, C. Le Conte de Poly-Barbut, Lines arrangements of reflections in Coxeter groups, Preprint, 2003
    • (2003)
    • Caspard, N.1    Crapo, H.2    Le Conte de Poly-Barbut, C.3
  • 9
    • 0343416304 scopus 로고
    • The classification of zonohedra by means of projective diagrams
    • Coxeter H.S.M. The classification of zonohedra by means of projective diagrams J. Math. Pures Appl. 41 1962 137-156
    • (1962) J. Math. Pures Appl. , vol.41 , pp. 137-156
    • Coxeter, H.S.M.1
  • 10
    • 0004232136 scopus 로고
    • Introduction to Lattices and Order
    • Cambridge University Press
    • Davey B.A. Priestley H.A. Introduction to Lattices and Order 1992 Cambridge University Press
    • (1992)
    • Davey, B.A.1    Priestley, H.A.2
  • 11
    • 0013327126 scopus 로고
    • A simple solution to the word problem for lattices
    • Day A. A simple solution to the word problem for lattices Canad. Math. Bull. 13 1970 253-254
    • (1970) Canad. Math. Bull. , vol.13 , pp. 253-254
    • Day, A.1
  • 12
    • 0003094802 scopus 로고
    • Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices
    • Day A. Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices, Canad. J. Math. 31 1979 69-78
    • (1979) Canad. J. Math. , vol.31 , pp. 69-78
    • Day, A.1
  • 13
    • 0141549806 scopus 로고
    • Doubling convex sets in lattices and a generalized semidistributivity condition
    • Order
    • Day A. Nation J.B. Tschantz S. Doubling convex sets in lattices and a generalized semidistributivity condition Order 6 1989 175-180
    • (1989) , vol.6 , pp. 175-180
    • Day, A.1    Nation, J.B.2    Tschantz, S.3
  • 14
    • 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 1994 397-406
    • (1994) Algebra Universalis , vol.31 , pp. 397-406
    • Day, A.1
  • 15
    • 0008561916 scopus 로고
    • The generalized doubling construction and formal concept analysis
    • Geyer W. The generalized doubling construction and formal concept analysis Algebra Universalis 32 1994 341-367
    • (1994) Algebra Universalis , vol.32 , pp. 341-367
    • Geyer, W.1
  • 17
    • 0003950889 scopus 로고
    • Reflection Groups and Coxeter Groups
    • Cambridge: Cambridge University Press
    • Humphreys J.E. Reflection Groups and Coxeter Groups 1990 Cambridge University Press Cambridge
    • (1990)
    • Humphreys, J.E.1
  • 19
    • 3142612665 scopus 로고    scopus 로고
    • Treillis de Cayley des groupes de Coxeter finis. Constructions par récurrence et décompositions sur des quotients
    • Le Conte de Poly-Barbut C. Treillis de Cayley des groupes de Coxeter finis. Constructions par récurrence et décompositions sur des quotients Math. Inf. Sci. Hum. 140 1997 11-33
    • (1997) Math. Inf. Sci. Hum. , vol.140 , pp. 11-33
    • Le Conte de Poly-Barbut, C.1
  • 20
    • 0001843738 scopus 로고
    • Equational bases and non-modular lattice varieties
    • McKenzie R. Equational bases and non-modular lattice varieties Trans. Amer. Math. Soc. 174 1972 1-43
    • (1972) Trans. Amer. Math. Soc. , vol.174 , pp. 1-43
    • McKenzie, R.1
  • 21
    • 0007345421 scopus 로고
    • Subdirect decomposition of concept lattices
    • Wille R. Subdirect decomposition of concept lattices Algebra Universalis 17 1983 275-287
    • (1983) Algebra Universalis , vol.17 , pp. 275-287
    • Wille, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.