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任意基数集上的拟阵的圈及连通性

Circuits and Connectivity of Matroids of Arbitrary Cardinality
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摘要 通过研究任意基数集上的拟阵圈的性质,继而得出当此拟阵连通时,它可由含任一给定元素的圈集唯一确定的结论. This paper deals with the properties of circuits of a matroid of arbitrary cardinality.Furthermore,it provides that when a matroid of arbitrary cardinality is connected,it is determined by the collection of circuits which contain a fixed element.
作者 毛华 俞珊珊
出处 《大学数学》 2010年第5期83-85,共3页 College Mathematics
基金 河北省教育厅科研项目(2006105) 河北大学省部共建项目(Y2005047)
关键词 任意基数集上的拟阵 连通的 直和 matroids of arbitrary cardinality circuit connected direct sum
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参考文献6

  • 1Welsh D J A. Matroid Thoery[M]. New York: Oxford University, 1992.
  • 2Oxley J. Infinite Matroids, Matroid Applications[M]. ed. by White N Cambridge: Cambridge University Press, 1992: 73-90.
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  • 5Mao H. Characterizations of Disconnected Matroids[J]. Algebra Colloquium, 2008, 15(1) : 129- 134.
  • 6毛华.任意基数集上的拟阵之单扩张[J].数学学报(中文版),2007,50(6):1271-1280. 被引量:2

二级参考文献10

  • 1Welsh D., Matroid theory, London: Academic Press Inc., 1976.
  • 2Oxley J., Matroid theory, New York: Oxford University Press, 1992.
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  • 5Betten D., Wenzel W., On linear spaces and matroids of arbitrary cardinality, Algebra Universalis, 2003, 49(3): 259-288.
  • 6Mao H., On geometric lattices and matroids of arbitrary cardinality, Ars Combinatoria, 2006, 81: 23-32.
  • 7Bonin J., Extending a matroid by a cocircuit, http://home.gwu.edu/jbonin/modhyp.ps
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  • 9Mao H., Characterization of disconnected matroids, Algebra Colloquium, in Press.
  • 10Gratzer G., General lattice theory, 2nd. ed., Basel: Birkhauser-Verlag, 1998.

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