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New Results on Global Rank Axioms of Poset Matroids

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Abstract

An excellent introduction to the topic of poset matroids is due to M. Barnabei, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rank axioms for poset matroids. In this paper, we study the special integral function f and obtain a new class of poset matroids from the old ones, and then we generalize this result according to the properties of f. Almost all of these results can be regarded as the application of global rank axioms for poset matroids. The main results in our paper have, indeed, investigated the restriction of the basis of the poset matroid, and we give them the corresponding geometric interpretation.

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Authors and Affiliations

  1. Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, P. R. China

    Shu Chao Li

  2. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

    Shu Chao Li

  3. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

    Yan Qin Feng

Authors
  1. Shu Chao Li
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  2. Yan Qin Feng
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Correspondence to Shu Chao Li.

Additional information

Supported partially by the National Natural Science Foundation of China (Grant No. 10371048)

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Li, S.C., Feng, Y.Q. New Results on Global Rank Axioms of Poset Matroids. Acta Math Sinica 21, 143–154 (2005). https://doi.org/10.1007/s10114-004-0411-6

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  • DOI: https://doi.org/10.1007/s10114-004-0411-6

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