{"id":"palomar/PALOMAR-2026-09-27-000003","url":"https://github.com/mmislan/palomar-p020-raf-abundant-reactions/tree/c1ebf53f80cc4a45af67142aa1e33f1a53494b8c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-27-000003-v1.json","repo":"https://github.com/mmislan/palomar-p020-raf-abundant-reactions","tags":["math.CO","q-bio.MN","msc:05D05","msc:92C42","msc:68V20","autocatalytic-sets","union-closed-sets","combinatorics","reaction-networks"],"score":0,"title":"Equivalence of the RAF abundance conjecture and Frankl's union-closed sets conjecture","trust":"high","domain":"math.CO","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.CO","summary":"In a catalytic reaction system with finitely many reactions, a RAF is a nonempty set of reactions whose reactants are produced from the food set by iterated closure under the selected reactions and whose reactions are each catalysed by a molecule of that closure. Steel (arXiv:2305.16714v4, Section 4) asked whether some reaction always lies in at least half of the RAFs. Call a reaction food-ready if all its reactants are food, and abundant if it lies in at least half of the sets in the family formed by the RAFs and the empty set. If some RAF U consists entirely of food-ready reactions, then…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true,"formalizes":[{"title":"Elementary cores, abundant reactions, and the union-closed boundary of autocatalytic reaction systems","identifier":"","relationship":"formalizes"}]}