Editing Matroid (section)

===Whitney numbers===
The ''Whitney numbers of the first kind'' of <math> M </math> are the coefficients of the powers of <math>\lambda</math> in the characteristic polynomial. Specifically, the <math>i</math>th Whitney number <math> w_i(M) </math> is the coefficient of <math>\lambda^{r(M)-i}</math> and is the sum of Möbius function values:
:<math>w_i(M) = \sum \{ \mu(\emptyset,A): r(A) = i \},</math>
summed over flats of the right rank. These numbers alternate in sign, so that <math>(-1)^i w_i(M) > 0</math> for <math>0 \leq i \leq r(M)</math>.

The ''Whitney numbers of the second kind'' of <math> M </math> are the numbers of flats of each rank. That is, <math> W_i(M) </math> is the number of rank&nbsp;<math>i</math> flats.

The Whitney numbers of both kinds generalize the [[Stirling number]]s of the first and second kind, which are the Whitney numbers of the cycle matroid of the [[complete graph]], and equivalently of the [[Partition of a set#Refinement_of_partitions|partition lattice]]. They were named after [[Hassler Whitney]], the (co)founder of matroid theory, by [[Gian-Carlo Rota]]. The name has been extended to the similar numbers for finite ranked [[partially ordered set]]s.