# fVector(Matroid) -- f-vector of a matroid

## Description

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 i2 : fVector M o2 = HashTable{0 => 1} 1 => 2 2 => 1 o2 : HashTable i3 : fVector matroid completeGraph 4 o3 = HashTable{0 => 1} 1 => 6 2 => 7 3 => 1 o3 : HashTable

## Caveat

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".