  We consider the Cartesian product X of n finite intervals of integers and a
map F from X to itself. As main result, we establish an upper bound on the
number of fixed points for F which only depends on X and on the topology of the
positive circuits of the interaction graph associated with F. The proof uses
and strongly generalizes a theorem of Richard and Comet which corresponds to a
discrete version of the Thomas' conjecture: if the interaction graph associated
with F has no positive circuit, then F has at most one fixed point. The
obtained upper bound on the number of fixed points also strongly generalizes
the one established by Aracena et al for a particular class of Boolean
networks.
