Some matroid inequalities

of M and Ik is the number of independent k-element sets in M. Note that W, = F(M), wher c /i(M) is the absolute value of the Miibius function p computed on the lattice of flats of M, and I, = b(M), the number of bases or complexity of M. Let C~ = min{(C( 1 C is a circuit in M). A..We say that M is loopless if c, > 1 and that M is a (combinatorial) geometry if c, > 2. In the sequel the letters r and n will always refer to the rank and cardinality respectively of the matroid being considered.