| Title:
|
Graph automorphisms and cells of lattices (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
103-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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). (English) |
| Keyword:
|
lattice |
| Keyword:
|
semimodular lattice |
| Keyword:
|
graph automorphism |
| Keyword:
|
direct factor |
| MSC:
|
06B05 |
| MSC:
|
06C10 |
| idZBL:
|
Zbl 1014.06007 |
| idMR:
|
MR1962002 |
| . |
| Date available:
|
2009-09-24T10:59:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127784 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] J. Jakubík: On graph isomorphism of lattices.Czechoslovak Math. J. 4 (1954), 131–142. (Russian) MR 0069139 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] J. Jakubík: Graph automorphisms of semimodular lattices.Math. Bohem. 125 (2000), 459–464. MR 1802294 |
| Reference:
|
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| Reference:
|
[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. Zbl 0563.06004, MR 0815129 |
| Reference:
|
[9] J. G. Lee: Covering graphs of lattices.Bull. Korean Math. Soc. 23 (1986), 39–46. Zbl 0606.06005, MR 0843207 |
| Reference:
|
[10] C. Ratanaprasert: Compatible Orderings of Semilattices and Lattices.Ph.D. Thesis, La Trobe University, 1987. |
| Reference:
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[11] C. Ratanaprasert: Compatible orders on semilattices.Tatra Mt. Math. Publ. 5 (1995), 177–187. MR 1384807 |
| Reference:
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[12] C. Ratanaprasert and B. A. Davey: Semimodular lattices with isomorphic graphs.Order 4 (1987), 1–13. MR 0908432 |
| Reference:
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[13] K. Reuter: The Kurosh-Ore exchange property.Acta Math. Acad. Sci. Hung. 53 (1989), 119–127. Zbl 0675.06003, MR 0987044, 10.1007/BF02170062 |
| Reference:
|
[14] M. Stern: On the covering graph of balanced lattices.Discrete Math. 156 (1996), 311–316. Zbl 0861.06005, MR 1405034, 10.1016/0012-365X(95)00061-Z |
| Reference:
|
[15] M. Tomková: Graph isomorphisms of partially ordered sets.Math. Slovaca 37 (1987), 47–52. MR 0899016 |
| Reference:
|
[16] R. Wille: Subdirect decompositions of concept lattices.Algebra Universalis 17 (1983), 275–287. MR 0729937, 10.1007/BF01194537 |
| . |
