Open Research Index

To cover a permutohedron

Bochao Kong

Palomar Registrypalomar/PALOMAR-2026-09-14-000004Sep 14, 2026math.COscore 0

This Lean 4 formalization of Kong and Zeng's To cover a permutohedron (arXiv:2509.13877v3, 9 April 2026) determines the minimum number of affine hyperplanes needed to cover the permutation vertices of (1,...,n), excluding the hyperplane containing every vertex. The exact answer is n for odd n at least 3, and n-1 for even n at least 4. It also proves that an arbitrary injective real tuple of length n at least 2 has the sharp hyperplane intersection bound (n-1)! when its n-1 signed critical values are distinct. Genuine polynomial-root path lifting establishes local transpositions and the cycle…

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