The f-vector of a matroid M is the invariant (f_0, f_1, ..., f_r), where f_i is the number of rank i flats of M, and r is the rank of M. Note that f_0 = f_r = 1, as the set of loops is the unique flat of rank 0, and the ground set is the unique flat of maximal rank.
i1 : M = matroid({a,b,c,d},{{a,b},{a,c}})
o1 = a matroid of rank 2 on 4 elements
o1 : Matroid
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i2 : fVector M
o2 = HashTable{0 => 1}
1 => 2
2 => 1
o2 : HashTable
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i3 : fVector matroid completeGraph 4
o3 = HashTable{0 => 1}
1 => 6
2 => 7
3 => 1
o3 : HashTable
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This is not the same as the f-vector of the independence complex of the matroid M, which counts the number of independent sets of a given size. To do this instead, use "fVector independenceComplex M".