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 b...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.展开更多
文摘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.
