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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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/

[1] Azanchiler H., “Extension of line-splitting operation from graphs to binary matroids”, Lobachevskii Journal of Mathematics, 24 (2006), 3–12 | MR | Zbl

[2] Fleischner H., Eulerian Graphs and Related Topics, Part 1, Vol. 1, North Holland, Amsterdam, 1990 | MR | Zbl

[3] Oxley J. G., Matroid Theory, Oxford University Press, New York, 1992 | MR | Zbl

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