  Growing network models have been shown to display emergent quantum statistics
when nodes are associated to a fitness value describing the intrinsic ability
of a node to acquire new links. Recently it has been shown that quantum
statistics emerge also in a growing simplicial complex model called Network
Geometry with Flavor which allow for the description of many-body interaction
between the nodes. This model depend on an external parameter called flavor
that is responsible for the underlying topology of the simplicial complex. When
the flavor takes the value $s=-1$ the $d$-dimensional simplicial complex is a
manifold in which every $(d-1)$-dimensional face can only have an incidence
number $n_{\alpha}\in\{0,1\}$. In this case the faces of the simplicial complex
are naturally described by the Bose-Einstein, Boltzmann and Fermi-Dirac
distribution depending on their dimension. In this paper we extent the study of
Network Geometry with Flavor to fractional values of the flavor $s=-1/m$ in
which every $(d-1)$-dimensional face can only have incidence number
$n_{\alpha}\in\{0,1,2,\dots, m\}$. We show that in this case the statistical
properties of the faces of the simplicial complex are described by the
Bose-Einstein or the Fermi-Dirac distribution only. Finally we comment on the
spectral properties of the networks constituting the underlying structure of
the considered simplicial complexes.
