Rigidity, Descents, and Cone Walks in Pattern-Avoiding Canon Permutations

Abstract

This preprint proves four conjectures on pattern avoidance in canon permutations, gives all twelve counting formulas for the 64 subsets of three-letter forbidden permutations at fixed alphabet size three, and determines principal descent factorizations. It also solves the intermediate repeated-endpoint enumeration by multichain and cone-walk methods and enumerates general alternating orbits by Davenport-Schinzel skeleton order polynomials. A Lean 4 formalization of the principal results is in progress; the present version does not claim completed formal verification.