Geodesic
Broken Circuits in Matroids—Dohmen’s Inductive Proof
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 599-602.

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Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids
Keywords: matroids, broken circuits, induction 
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Kordecki, Wojciech; Łyczkowska-Hanćkowiak, Anna. Broken Circuits in Matroids—Dohmen’s Inductive Proof. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 599-602. http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a8/

[1] T. Brylawski, The broken circuit complex, Trans. Amer. Math. Soc. 234 (1977) 417-433. doi:10.1090/S0002-9947-1977-0468931-6

[2] T. Brylawski and J. Oxley, The Tutte polynomials and its applications, in: Matroid Applications, N. White (Ed(s)), (Cambridge University Press, 1992) 121-225.

[3] K. Dohmen, Some remarks on the sieve formula, the Tutte polynomial and Crapo’s beta invariant, Aequationes Math. 60 (2000) 108-115. doi:10.1007/s000100050139

[4] K. Dohmen, An inductive proof of Whitneys broken circuit theorem, Disscus. Math. Graph Theory 31 (2011) 509-515. doi:10.7151/dmgt.1561

[5] A.P. Heron, Matroid polynomials, in: Combinatorics, D.J.A. Welsh and D.R. Woodall (Ed(s)), (The Institute of Combinatorics and Its Applications, Southend-On-Sea, 1972) 164-202.

[6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).