{"paper":{"title":"Number of fixed points and disjoint cycles in monotone Boolean networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.IT","q-bio.MN"],"primary_cat":"math.CO","authors_text":"Adrien Richard, Julio Aracena, Lilian Salinas","submitted_at":"2016-02-09T18:15:30Z","abstract_excerpt":"Given a digraph $G$, a lot of attention has been deserved on the maximum number $\\phi(G)$ of fixed points in a Boolean network $f:\\{0,1\\}^n\\to\\{0,1\\}^n$ with $G$ as interaction graph. In particular, a central problem in network coding consists in studying the optimality of the classical upper bound $\\phi(G)\\leq 2^{\\tau}$, where $\\tau$ is the minimum size of a feedback vertex set of $G$. In this paper, we study the maximum number $\\phi_m(G)$ of fixed points in a {\\em monotone} Boolean network with interaction graph $G$. We establish new upper and lower bounds on $\\phi_m(G)$ that depends on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03109","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}