{"id":"palomar/PALOMAR-2026-10-28-000003","url":"https://github.com/jtraverso/kirkman-steiner-triple-systems/tree/18551414d822f7fa4fb7535dc43733c4b316c3a8","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000003-v1.json","repo":"https://github.com/jtraverso/kirkman-steiner-triple-systems","tags":["math.CO","msc:05B07"],"score":0,"title":"Kirkman's theorem on Steiner triple systems","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of Kirkman's 1847 theorem: for v ≥ 1, a Steiner triple system on v points (a family of 3-subsets covering every pair of distinct points exactly once) exists if and only if v ≡ 1 or 3 (mod 6). Sufficiency is proved by Bose's and Skolem's constructions from Steiner quasigroups. Mathlib does not contain Steiner triple systems.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"On a problem in combinations","identifier":"","relationship":"formalizes"}]}