发表机构
Qufu Normal University; China University of Petroleum（曲阜师范大学; 中国石油大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造2143-与3421-避免排列间的显式双射，证明Burstein猜想，保持尖峰集并反转尖峰顺序，进而证明Dumont排列上的Wilf等价性。
AI 中文摘要
我们通过构造两个避免类之间的显式双射，证明了Burstein关于下降峰顶集分布的猜想在2143-3421情形下的成立。该双射还保持尖峰集，并反转尖峰值的从左到右顺序。我们将最大笛卡尔树上的对合与最大递减序列最后条目的交换相结合。在一个中间避免类上，我们证明了交换过程会终止，并且每个方向的输出与所做的选择无关。这给出了一个显式逆映射。将该双射限制在第一类Dumont排列上，证明了Burstein和Jones的猜想，即2143和3421在这一类上是Wilf等价的。
英文摘要
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
