Geodesic
A characterization of the bases of line-splitting matroids
Lobachevskii journal of mathematics, Tome 26 (2007), pp. 5-15

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In [1] the author extended $n$-line splitting from graphs to binary matroids and characterized the circuits of the result matroid, i.e. line-splitting matroid (es-splitting). In this paper, we characterize dependent, independent and base sets in line-splitting matroid $M_X^e$. Moreover, we determine rank function of $M_X^e$. 
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     author = {H. Azanchiler},
     title = {A characterization of the bases of line-splitting matroids},
     journal = {Lobachevskii journal of mathematics},
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     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_26_a1/}
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H. Azanchiler. A characterization of the bases of line-splitting matroids. Lobachevskii journal of mathematics, Tome 26 (2007), pp. 5-15. http://geodesic.mathdoc.fr/item/LJM_2007_26_a1/