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On the rank functions of $\mathcal{H}$-matroids

Year 2016, , 7 - 11, 11.01.2016
https://doi.org/10.13069/jacodesmath.26764

Abstract

The notion of $\mathcal{H}$-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of $\mathcal{H}$-matroids by the greedy algorithm. In this note, we give a characterization of some $\mathcal{H}$-matroids by rank functions.

References

  • U. Faigle, S. Fujishige, A general model for matroids and the greedy algorithm, Math. Program. Ser.
  • A 119(2) (2009) 353–369.
  • S. Fujishige, Submodular functions and optimization, Annals of Discrete Mathematics, Elsevier, Amsterdam, 2005.
  • S. Fujishige, G. A. Koshevoy, Y. Sano, Matroids on convex geometries (cg-matroids), Discrete Math. 307(15) (2007) 1936–1950.
  • B. Korte, L. Lovász, R. Schrader, Greedoids, Algorithms and combinatorics, Vol. 4, Springer-Verlag, Berlin, 1991.
  • J. Oxley, Matroid theory, Oxford University Press, Oxford, 1992.
  • Y. Sano, Rank functions of strict cg-matroids, Discrete Math. 38(20) (2008) 4734–4744.
  • Y. Sano, Matroids on convex geometries: subclasses, operations, and optimization, Publ. Res. Inst.
  • Math. Sci. 47(3) (2011) 671–703.
  • A. Schrijver, Combinatorial optimization. Polyhedra and Efficiency, Algorithms and Combinatorics, Vol. 24, Springer-Verlag, Berlin, 2003.
  • D. J. A. Welsh, Matroid theory, Academic Press, London, 1976.
  • H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57(3) (1935) 509–533.

2010 MSC: 05B35, 90C27

Year 2016, , 7 - 11, 11.01.2016
https://doi.org/10.13069/jacodesmath.26764

Abstract

References

  • U. Faigle, S. Fujishige, A general model for matroids and the greedy algorithm, Math. Program. Ser.
  • A 119(2) (2009) 353–369.
  • S. Fujishige, Submodular functions and optimization, Annals of Discrete Mathematics, Elsevier, Amsterdam, 2005.
  • S. Fujishige, G. A. Koshevoy, Y. Sano, Matroids on convex geometries (cg-matroids), Discrete Math. 307(15) (2007) 1936–1950.
  • B. Korte, L. Lovász, R. Schrader, Greedoids, Algorithms and combinatorics, Vol. 4, Springer-Verlag, Berlin, 1991.
  • J. Oxley, Matroid theory, Oxford University Press, Oxford, 1992.
  • Y. Sano, Rank functions of strict cg-matroids, Discrete Math. 38(20) (2008) 4734–4744.
  • Y. Sano, Matroids on convex geometries: subclasses, operations, and optimization, Publ. Res. Inst.
  • Math. Sci. 47(3) (2011) 671–703.
  • A. Schrijver, Combinatorial optimization. Polyhedra and Efficiency, Algorithms and Combinatorics, Vol. 24, Springer-Verlag, Berlin, 2003.
  • D. J. A. Welsh, Matroid theory, Academic Press, London, 1976.
  • H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57(3) (1935) 509–533.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Yoshio Sano This is me

Publication Date January 11, 2016
Published in Issue Year 2016

Cite

APA Sano, Y. (2016). On the rank functions of $\mathcal{H}$-matroids. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(1), 7-11. https://doi.org/10.13069/jacodesmath.26764
AMA Sano Y. On the rank functions of $\mathcal{H}$-matroids. Journal of Algebra Combinatorics Discrete Structures and Applications. January 2016;3(1):7-11. doi:10.13069/jacodesmath.26764
Chicago Sano, Yoshio. “On the Rank Functions of $\mathcal{H}$-Matroids”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, no. 1 (January 2016): 7-11. https://doi.org/10.13069/jacodesmath.26764.
EndNote Sano Y (January 1, 2016) On the rank functions of $\mathcal{H}$-matroids. Journal of Algebra Combinatorics Discrete Structures and Applications 3 1 7–11.
IEEE Y. Sano, “On the rank functions of $\mathcal{H}$-matroids”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 1, pp. 7–11, 2016, doi: 10.13069/jacodesmath.26764.
ISNAD Sano, Yoshio. “On the Rank Functions of $\mathcal{H}$-Matroids”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/1 (January 2016), 7-11. https://doi.org/10.13069/jacodesmath.26764.
JAMA Sano Y. On the rank functions of $\mathcal{H}$-matroids. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:7–11.
MLA Sano, Yoshio. “On the Rank Functions of $\mathcal{H}$-Matroids”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 1, 2016, pp. 7-11, doi:10.13069/jacodesmath.26764.
Vancouver Sano Y. On the rank functions of $\mathcal{H}$-matroids. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(1):7-11.