Descent Tops and Pinnacles on 2143- and 3421-Avoiding Permutations
Yue Dong, Lily Li Liu, Tongyuan Zhao
Source abstract
We prove the 2143-3421 case of Burstein's conjecture on the distribution of descent-top sets by constructing an explicit bijection between the two avoidance classes. The bijection also preserves the pinnacle set and reverses the left-to-right order of the pinnacle values. We combine an involution on maximum Cartesian trees with exchanges of the final entries of maximal decreasing runs. On an intermediate avoidance class, we prove that the exchange procedures terminate and that the output in each direction is independent of the choices made. This gives an explicit inverse. Restricting the bijection to Dumont permutations of the first kind proves the conjecture of Burstein and Jones that 2143 and 3421 are Wilf-equivalent on this class
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.