Geodesic
Graph automorphisms and cells of lattices
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 103-111 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).
In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).
Classification : 06B05, 06C10
Keywords: lattice; semimodular lattice; graph automorphism; direct factor 
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Jakubík, Ján. Graph automorphisms and cells of lattices. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 103-111. http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a8/

[1] G.  Birkhoff: Lattice Theory. Third Edition, , Providence, 1967. | MR | Zbl

[2] D.  Duffus and I.  Rival: Path length in the covering graph of a lattice. Discrete Math. 19 (1979), 139–158. | DOI | MR

[3] J. Jakubík: On graph isomorphism of lattices. Czechoslovak Math.  J. 4 (1954), 131–142. (Russian) | MR

[4] J. Jakubík: On isomorphisms of graphs of lattices. Czechoslovak Math.  J. 35 (1985), 188–200. | MR

[5] J.  Jakubík: Graph automorphisms of a finite modular lattice. Czechoslovak Math.  J. 49 (1999), 443–447. | DOI | MR

[6] J.  Jakubík: Graph automorphisms of semimodular lattices. Math. Bohem. 125 (2000), 459–464. | MR

[7] J.  Jakubík and M.  Csontóová: Convex isomorphisms of directed multilattices. Math. Bohem. 118 (1993), 359–379. | MR

[8] M.  Kolibiar: Graph isomorphisms of semilattices. In: Contributions to General Algebra  3, Proc. of the Vienna Conference 1984, Verlag Hölder-Pichler-Tempsky, Wien, 1985, pp. 225–235. | MR | Zbl

[9] J. G.  Lee: Covering graphs of lattices. Bull. Korean Math. Soc. 23 (1986), 39–46. | MR | Zbl

[10] C.  Ratanaprasert: Compatible Orderings of Semilattices and Lattices. Ph.D. Thesis, La Trobe University, 1987.

[11] C.  Ratanaprasert: Compatible orders on semilattices. Tatra Mt. Math. Publ. 5 (1995), 177–187. | MR

[12] C.  Ratanaprasert and B. A.  Davey: Semimodular lattices with isomorphic graphs. Order 4 (1987), 1–13. | MR

[13] K.  Reuter: The Kurosh-Ore exchange property. Acta Math. Acad. Sci. Hung. 53 (1989), 119–127. | DOI | MR | Zbl

[14] M.  Stern: On the covering graph of balanced lattices. Discrete Math. 156 (1996), 311–316. | DOI | MR | Zbl

[15] M.  Tomková: Graph isomorphisms of partially ordered sets. Math. Slovaca 37 (1987), 47–52. | MR

[16] R.  Wille: Subdirect decompositions of concept lattices. Algebra Universalis 17 (1983), 275–287. | DOI | MR