Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 126345, 6 pages
http://dx.doi.org/10.1155/2014/126345
Research Article

Base Axioms of Modular Supermatroids

School of Mathematics and Statistics, Xidian University, Xi’an 710071, China

Received 15 October 2013; Accepted 19 January 2014; Published 5 March 2014

Academic Editor: Shiping Lu

Copyright © 2014 Xiaonan Li and Sanyang Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Edmonds, “Submodular functions, matroids and certain polyhedra,” in Proceedings of the Calgary International Conference on Combinatorial Structures and Their Applications, pp. 69–87, Gordon and Breach, New York, NY, USA, 1969.
  2. F. D. J. Dunstan, A. W. Ingleton, and D. J. A. Welsh, “Supermatroids,” in Proceedings of the conference on Combinatorial Mathematics, pp. 72–122, Mathematical Institute, Oxford, UK, 1972.
  3. B. Korte, L. Lovsz, and R. Schrader, Greedords, Springer, Berlin, Germany, 1991.
  4. R. Goetschel, and W. Voxman, “Fuzzy matroids,” Fuzzy Sets and Systems, vol. 27, no. 3, pp. 291–302, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  5. U. Faigle, “Geometries on partially ordered sets,” Journal of Combinatorial Theory B, vol. 28, no. 1, pp. 26–51, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  6. E. Tardos, “An intersection theorem for supermatroids,” Journal of Combinatorial Theory B, vol. 50, no. 2, pp. 150–159, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Barnabei, G. Nicoletti, and L. Pezzoli, “Matroids on partially ordered sets,” Advances in Applied Mathematics, vol. 21, no. 1, pp. 78–112, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Fujishige, G. A. Koshevoy, and Y. Sano, “Matroids on convex geometries,” Discrete Mathematics, vol. 307, no. 15, pp. 1936–1950, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Wild, “Weakly submodular rank functions, supermatroids, and the flat lattice of a distributive supermatroid,” Discrete Mathematics, vol. 308, no. 7, pp. 999–1017, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S.-G. Li, X. Xin, and Y.-L. Li, “Closure axioms for a class of fuzzy matroids and co-towers of matroids,” Fuzzy Sets and Systems, vol. 158, no. 11, pp. 1246–1257, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Y. Sano, “Rank functions of strict cg-matroids,” Discrete Mathematics, vol. 308, no. 20, pp. 4734–4744, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  12. W. Yao and F.-G. Shi, “Bases axioms and circuits axioms for fuzzifying matroids,” Fuzzy Sets and Systems, vol. 161, no. 24, pp. 3155–3165, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. D. J. A. Welsh, Matroid Theory, Academic Press, London, UK, 1976. View at MathSciNet
  14. S. Roman, Lattice and Ordered, Springer, New York, NY, USA, 2008.
  15. N. White, Ed., Theory of Matroids, Cambridge University Press, Cambridge, UK, 1986.