  In network coding, a flag code is a collection of flags, that is, sequences
of nested subspaces of a vector space over a finite field. Due to its
definition as the sum of the corresponding subspace distances, the flag
distance parameter encloses a hidden combinatorial structure. To bring it to
light, in this paper, we interpret flag distances by means of distance paths
drawn in a convenient distance support. The shape of such a support allows us
to create an ad hoc associated Ferrers diagram frame where we develop a
combinatorial approach to flag codes by relating the possible realizations of
their minimum distance to different partitions of appropriate integers. This
novel viewpoint permits to establish noteworthy connections between the flag
code parameters and the ones of its projected codes in terms of well known
concepts coming from the classical partitions theory.
