Main Article Content
Abstract
Using the Hasse diagrams of concept lattices, we investigate the
relations between matroids and geometric contexts, followed by
judging a mathematical construction to be a matroid. We provide an
idea to find out the dual of a matroid from the ways of concept
lattice drawing. In addition, we utilize the Hasse diagrams of
concept lattices to discuss the minors of matroids, direct sum of
matroids and the connectivity of a matroid. All the consequences
demonstrate that the theory of concept lattice drawing can be used
into matroids. This generalizes the applied fields of concept
lattices.
Keywords
Article Details
References
- bibitem{1} Faigle, U. and Fujishige, S., ``A general model for matroids
- and the greedy algorithm", {em Math. Prog., ser. A}
- textbf{119}(2)(2009), 353 - 369.
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- drawing", http://www.math.hawaii.edu/$sim$ralph
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- Heildelberg, 2005.
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- bibitem{7} 9th. International Conference on Formal Concept
- Analysis, Nicosia, Cyprus, May 2-6, 2011.
- bibitem{8} Lai, H.J., {it Matroid Theory}, Hingher Education
- Press, Beijing, 2002.(in Chinese)
- bibitem{9}Mao, H., ``An approach to access to a concept lattice
- via the idea of lattice theory", {em Univ. Politehnica of Bucharest
- Sci. Bull., series A, Math. and Phys.} textbf{73}(2)(2011), 37 -
- bibitem{10} Mao, H., ``Complete atomistic lattices are classification
- lattices", Algeb. Univ. textbf{68}(3-4)(2012), 293 - 294.
- bibitem{11} Mao, H., ``On closure axioms for a matroid using Galois
- connections", {em Math. Commu.} textbf{14}(2)(2009), 425 - 432.
- bibitem{12} Mao, H., ``On lattice-theoretical construction of
- matroids", {em Anna. of the Alexandru loan Cuza University-Math.}
- textbf{59}(1)(2013), 201 - 208.
- bibitem{13} Owais, S., Gajdov s, P. and Sn' av sel, V., ``Usage of
- genetic algorithm for lattice drawing", Radim Bv elohl'avek,
- V'aclav Sn'av sel(eds.): {it CLA 2005}, 82-91.
- bibitem{14} Oxley, J., {it Matroid Theory}, 2nd. ed., Oxford University
- Press, New York, 2011.
- bibitem{15}Stumme, G. and Wille, R., ``A geometrical heuristic
- for drawing concept lattices", {em Lect. Note. in Compu.
- Sci.} textbf{894}(1995), 452 - 459.
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- {it Matroid Theory}, Academic Press, London, 1976.
References
bibitem{1} Faigle, U. and Fujishige, S., ``A general model for matroids
and the greedy algorithm", {em Math. Prog., ser. A}
textbf{119}(2)(2009), 353 - 369.
bibitem{2}Freese, R., ``Automated lattice
drawing", http://www.math.hawaii.edu/$sim$ralph
bibitem{3} Ganter, B., Stumme, G. and Wille, R., (eds.), {it Formal Concept
Analysis: Foundations and Applications}, Springer-Verlag Berlin,
Heildelberg, 2005.
bibitem{4} Ganter, B. and Wille, R., {it Formal Concept
Analysis: Mathematical Foundations}, Springer-Verlag Berlin,
Heidelberg, 1999.
bibitem{5} Gr"azter, G., {it Lattice Theory}, 2nd., Birkh"auser Verlag, Basel, 1998.
bibitem{6} Gr"azter, G., {it Lattice Theory: Foundation},
Springer Basel AG, Berlin, 2011.
bibitem{7} 9th. International Conference on Formal Concept
Analysis, Nicosia, Cyprus, May 2-6, 2011.
bibitem{8} Lai, H.J., {it Matroid Theory}, Hingher Education
Press, Beijing, 2002.(in Chinese)
bibitem{9}Mao, H., ``An approach to access to a concept lattice
via the idea of lattice theory", {em Univ. Politehnica of Bucharest
Sci. Bull., series A, Math. and Phys.} textbf{73}(2)(2011), 37 -
bibitem{10} Mao, H., ``Complete atomistic lattices are classification
lattices", Algeb. Univ. textbf{68}(3-4)(2012), 293 - 294.
bibitem{11} Mao, H., ``On closure axioms for a matroid using Galois
connections", {em Math. Commu.} textbf{14}(2)(2009), 425 - 432.
bibitem{12} Mao, H., ``On lattice-theoretical construction of
matroids", {em Anna. of the Alexandru loan Cuza University-Math.}
textbf{59}(1)(2013), 201 - 208.
bibitem{13} Owais, S., Gajdov s, P. and Sn' av sel, V., ``Usage of
genetic algorithm for lattice drawing", Radim Bv elohl'avek,
V'aclav Sn'av sel(eds.): {it CLA 2005}, 82-91.
bibitem{14} Oxley, J., {it Matroid Theory}, 2nd. ed., Oxford University
Press, New York, 2011.
bibitem{15}Stumme, G. and Wille, R., ``A geometrical heuristic
for drawing concept lattices", {em Lect. Note. in Compu.
Sci.} textbf{894}(1995), 452 - 459.
bibitem{16} Welsh, D.J.A.,
{it Matroid Theory}, Academic Press, London, 1976.