Previous |  Up |  Next

Article

Title: Some properties of Eulerian lattices (English)
Author: Subbarayan, R.
Author: Vethamanickam, A.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 55
Issue: 4
Year: 2014
Pages: 499-507
Summary lang: English
.
Category: math
.
Summary: In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean. (English)
Keyword: Eulerian lattices
Keyword: 0-distributive lattices
Keyword: pseudo-0-distributive lattices
Keyword: super-0-distributive lattices
MSC: 03G10
MSC: 06A06
MSC: 06A07
idZBL: Zbl 06391558
idMR: MR3269012
.
Date available: 2014-10-09T09:56:52Z
Last updated: 2017-01-02
Stable URL: http://hdl.handle.net/10338.dmlcz/143974
.
Reference: [1] Balasubramani P.: Stone topologies of the set of prime filters of a $0$-distributive lattice.Indian J. Pure Appl. Math. 35 (2004), no. 2, 149–158. MR 2040729
Reference: [2] Bayer M., Billera J.: Counting chains and faces in polytopes and posets.Contemporary Mathematics 34 (1984), 207-252. 10.1090/conm/034/777703
Reference: [3] Chajda I., Radeleczki S.: $0$-conditions and tolerance schemes.Acta Math. Univ. Comenian. 72 (2003), no. 2, 177–184. Zbl 1087.08002, MR 2040261
Reference: [4] Crawley P., Dilworth R.P.: Algebraic Theory of Lattices.Prentice-Hall, Inc., Englewod. Cliffs, New Jersey, 1973. Zbl 0494.06001
Reference: [5] Davey B.A., Priestley H.A.: Introduction to Lattices and Order.Second Edition, Cambridge University Press, Cambridge, 2002. Zbl 1002.06001, MR 1902334
Reference: [6] Gragg K.M., Kung J.P.S.: Consistent dually semimodular lattices.J. Combin. Theory Ser. A 60 (1992), 246–263. Zbl 0822.06007, MR 1168156, 10.1016/0097-3165(92)90006-G
Reference: [7] Grätzer G.: General Lattice Theory.Birkhäuser, Basel, 1978. MR 0504338
Reference: [8] Grünbaum B.: Convex Polytopes.Interscience, London-New York, 1967. Zbl 1033.52001, MR 0226496
Reference: [9] Pawar Y.S.: $0$-$1$-distributive lattices.Indian J. Pure Appl. Math. 24 (1993), no. 3, 173–178. Zbl 0765.06015, MR 1210389
Reference: [10] Mckenzie R.N., Mcnulty G.E., Tayler W.F.: Algebras, Lattices, Varieties, Vol I.Wardswoth and Brooks/Cole, Monterey, California, 1987.
Reference: [11] Rota G.C.: On the foundations of combinatorial theory I. Theory of Möbius functions.Z. Wahrschainlichkeitstheorie und Verw. Gebiete 2 (1964), 340-368. Zbl 0121.02406, MR 0174487, 10.1007/BF00531932
Reference: [12] Santhi V. K.: Topics in Commutative Algebra.Ph.D. thesis, Madurai Kamaraj University, 1992.
Reference: [13] Subbarayan R.: Lattice Theory.Ph.D thesis, Bharathidasan University, 2008.
Reference: [14] Stanley R.P.: Some aspects of groups acting on finite posets.J. Combin. Theory Ser. A 32 (1982), 131–161. Zbl 0496.06001, MR 0654618, 10.1016/0097-3165(82)90017-6
Reference: [15] Stanley R.P.: Enumerative Combinatorics, Vol. 1.Wordsworth and Brooks/Cole, Monterey, CA, 1986. Zbl 1247.05003, 10.1007/978-1-4615-9763-6
Reference: [16] Stanley R.P.: Supersolvable lattices.Algebra Universalis 4 (1974), 361–371. Zbl 0256.06002, MR 0354473
Reference: [17] Varlet J.C.: A generalization of the notion of pseudo-complimentedness.Bull. Soc. Roy. Sci. Liège, 37 (1968), 149–158. MR 0228390
Reference: [18] Vethamanickam A.: Topics in Universal Algebra.Ph.D. thesis, Madurai Kamaraj University, 1994.
Reference: [19] Vethamanickam A., Subbarayan R.: Some simple extensions of Eulerian lattices.Acta Math. Univ. Comenianae 79 (2010), no. 1, 47–54. Zbl 1212.06007, MR 2684207
Reference: [20] Walendziak A.: On consistent lattices.Acta Sci. Math. (Szeged) 59 (1994), 49–52. Zbl 0803.06006, MR 1285428
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_55-2014-4_7.pdf 216.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo