کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
420825 | 683987 | 2006 | 7 صفحه PDF | دانلود رایگان |
Let M=(E,F)M=(E,F) be a rank-n matroid on a set E and B one of its bases. A closed set θ⊆Eθ⊆E is saturated with respect to B, or B -saturated, when |θ∩B|=r(θ)|θ∩B|=r(θ), where r(θ)r(θ) is the rank of θθ.The collection of subsets I of E such that |I∩θ|⩽r(θ)|I∩θ|⩽r(θ), for every closed B -saturated set θθ, turns out to be the family of independent sets of a new matroid on E , called base-matroid and denoted by MBMB. In this paper we prove some properties of MBMB, in particular that it satisfies the base-axiom of a matroid.Moreover, we determine a characterization of the matroids M which are isomorphic to MBMB for every base B of M.Finally, we prove that the poset of the closed B -saturated sets ordered by inclusion is isomorphic to the Boolean lattice BnBn.
Journal: Discrete Applied Mathematics - Volume 154, Issue 9, 1 June 2006, Pages 1401–1407