Two Results on Binary Matroids

Sun Liang, Zhao Jun, Yang Gang. Two Results on Binary Matroids[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1998, 7(1): 1-5.

Citation:

Sun Liang, Zhao Jun, Yang Gang. Two Results on Binary Matroids[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1998, 7(1): 1-5.

Citation:

Sun Liang, Zhao Jun, Yang Gang. Two Results on Binary Matroids[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1998, 7(1): 1-5.

Abstract

Aim To research new characterization and circuit property of binary matroid. Methods Constract the modular pairs of hyperplanes of a a matroid. Results and Conclusion It is proved that a matroid M on finite set S is binary if and only if for any two distinct hyper-planes H1 and H2, if H1H2S ,and H1 and H2 are modular pair, then S-(H1H2) is a hyperplande .And a necessary and sufficient condition for a binary matroid to have a k-circuit is obtained.

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