Open Research Index

Chain returns and lower bounds for superpermutations

Jay Pantone

Palomar Registrypalomar/PALOMAR-2026-10-27-000005Oct 27, 2026math.COscore 0

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.

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