2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208513We 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.13 pagesDiscrete MathematicsG.2.1; G.2.2; F.1.1text