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Abstract:

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset. © 2007 Springer Science + Business Media B.V.

Registro:

Documento: Artículo
Título:2-Dimension from the topological viewpoint
Autor:Barmak, J.A.; Minian, E.G.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:2-dimension; Finite topological spaces; Posets
Año:2007
Volumen:24
Número:1
Página de inicio:49
Página de fin:58
DOI: http://dx.doi.org/10.1007/s11083-007-9057-1
Título revista:Order
Título revista abreviado:Order
ISSN:01678094
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678094_v24_n1_p49_Barmak

Referencias:

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  • Barmak, J.A., Minian, E.G., (2006) Minimal Finite Models, , in press
  • Bourbaki, N., (1966) General Topology (I-II), , Addison-Wesley Reading
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  • Habib, M., Nourine, L., Raynaud, O., Thierry, E., Computational aspects of the 2-dimension of partially ordered sets (2004) Theor. Comp. Sci., 312, pp. 401-431
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  • May, J.P., Finite groups and finite spaces (2003) Notes for REU, , Department of Mathematics, The University of Chicago
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  • Novák, V., On the pseudo-dimension of ordered sets (1963) Czechoslovak Math. J., 13, pp. 587-598
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  • Stong, R.E., Finite topological spaces (1966) Trans. Am. Math. Soc., 123, pp. 325-340
  • Trotter, W.T., Embedding finite posets in cubes (1975) Discrete Math., 12, pp. 165-172
  • Trotter, W.T., (1991) Combinatorics and Partially Ordered Sets: Dimension Theory, , John Hopkins University Press Baltimore
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Citas:

---------- APA ----------
Barmak, J.A. & Minian, E.G. (2007) . 2-Dimension from the topological viewpoint. Order, 24(1), 49-58.
http://dx.doi.org/10.1007/s11083-007-9057-1
---------- CHICAGO ----------
Barmak, J.A., Minian, E.G. "2-Dimension from the topological viewpoint" . Order 24, no. 1 (2007) : 49-58.
http://dx.doi.org/10.1007/s11083-007-9057-1
---------- MLA ----------
Barmak, J.A., Minian, E.G. "2-Dimension from the topological viewpoint" . Order, vol. 24, no. 1, 2007, pp. 49-58.
http://dx.doi.org/10.1007/s11083-007-9057-1
---------- VANCOUVER ----------
Barmak, J.A., Minian, E.G. 2-Dimension from the topological viewpoint. Order. 2007;24(1):49-58.
http://dx.doi.org/10.1007/s11083-007-9057-1