{"id":"palomar/PALOMAR-2026-10-27-000005","url":"https://github.com/jaypantone/2026-10-superpermutation-lower-palomar/tree/8cc371be7ad7dc47252e45ffbda633a85776d596","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-27-000005-v1.json","repo":"https://github.com/jaypantone/2026-10-superpermutation-lower-palomar","tags":["math.CO","msc:05A05","msc:68R15","msc:03B35"],"score":0,"title":"Chain returns and lower bounds for superpermutations","trust":"high","domain":"math.CO","source":"palomar","authors":["Jay Pantone"],"reviews":0,"subject":"math.CO","summary":"Prove explicit general lower bounds for the shortest superpermutation length S(n), valid for every n >= 8. The exact-order and quadratic-order formulas refine the lower-order terms while retaining leading correction (2+o(1))(n-4)! above n!+(n-1)!+(n-2)!. The development also proves asymptotic comparisons with earlier general formulas; the selected theorem statements specify their exact scope. Separate finite refinements prove S(10) >= 4033379 and S(14) >= 93891141150.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-27","reactions":{},"formalized":true,"formalizes":[{"title":"Chain returns and lower bounds for superpermutations","identifier":"https://github.com/jaypantone/2026-10-superpermutation-bounds/tree/c9ccb6a0d9ddd1007fdce6efab50807ec47464b9/papers/lower/lower-bounds.tex","relationship":"formalizes"},{"title":"Three finite lower bounds for superpermutations","identifier":"https://github.com/jaypantone/2026-10-superpermutation-bounds/tree/c9ccb6a0d9ddd1007fdce6efab50807ec47464b9/papers/finite/finite-lower-bounds.tex","relationship":"formalizes"}]}