  It is shown that matroid theory may provide a natural mathematical framework
for a duality symmetries not only for quantum Yang-Mills physics, but also for
M-theory. Our discussion is focused in an action consisting purely of the
Chern-Simons term, but in principle the main ideas can be applied beyond such
an action. In our treatment the theorem due to Thistlethwaite, which gives a
relationship between the Tutte polynomial for graphs and Jones polynomial for
alternating knots and links, plays a central role. Before addressing this
question we briefly mention some important aspects of matroid theory and we
point out a connection between the Fano matroid and D=11 supergravity. Our
approach also seems to be related to loop solutions of quantum gravity based in
Ashtekar formalism.
