2008/07/26 by Adrien Richard, Richard, Adrien
Biochemistry, Genetics and Molecular Biology · #Bacterial Genetics and Biotechnology #Discrete Mathematics (cs.DM) #F.1.1 #FOS: Computer and information sciences #G.2.1 #G.2.2 #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction
paper · pdf · doi:10.48550/arxiv.0807.4229
openalex publication_date 2008/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.