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===Permutations are maximal flags===
There are ''n''! permutations of a set with ''n'' elements, and [''n'']!<sub>''q''</sub> maximal [[Flag (linear algebra)|flags]] in '''F'''{{su|b=''q''|p=''n''}}, where
:<math>[n]
is the [[Q-Pochhammer symbol#Relationship to other q-functions|''q''-factorial]]. Indeed, a permutation of a set can be considered a [[Filtration (mathematics)#Sets|filtered set]], as a flag is a filtered vector space: for instance, the ordering {{nowrap|(0, 1, 2)}} of the set {0, 1, 2} corresponds to the filtration {0} ⊂ {0,1} ⊂ {0,1,2}.
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