Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids
@article{bwmeta1.element.doi-10_7151_dmgt_1689,
author = {Wojciech Kordecki and Anna \L yczkowska-Han\'ckowiak},
title = {Broken Circuits in Matroids-Dohmen's Inductive Proof},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {599-602},
zbl = {1275.05021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1689}
}
Wojciech Kordecki; Anna Łyczkowska-Hanćkowiak. Broken Circuits in Matroids-Dohmen’s Inductive Proof. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 599-602. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1689/
[1] T. Brylawski, The broken circuit complex , Trans. Amer. Math. Soc. 234 (1977) 417-433. doi:10.1090/S0002-9947-1977-0468931-6[Crossref] | Zbl 0368.05022
[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. | Zbl 0769.05026
[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[Crossref] | Zbl 0959.05002
[4] K. Dohmen, An inductive proof of Whitneys broken circuit theorem, Disscus. Math. Graph Theory 31 (2011) 509-515. doi:10.7151/dmgt.1561[Crossref]
[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).