A permutation whose any prefix has no more descents than ascents is called a ballot permutation. In this paper, we present a decomposition of ballot permutations that enables us to construct a bijection between ballot permutations and odd order permutations, which proves a set-valued extension of a conjecture due to Spiro using the statistic of peak values. This bijection also preserves the neighbors of the largest letter in permutations and thus resolves a refinement of Spiro's conjecture proposed by Wang and Zhang. Our decomposition can be extended to well-labeled positive paths, a class of generalized ballot permutations arising from polytope theory, that were enumerated by Bernardi, Duplantier and Nadeau.

We will also investigate the enumerative aspect of ballot permutations avoiding a single pattern of length 3 and establish a connection between 213-avoiding ballot permutations and Gessel walks.

任何前缀的下降不超过上升的排列称为选票排列。在本文中，我们提出了选票排列的分解，使我们能够构建选票排列和奇数排列之间的双射，这证明了 Spiro 使用峰值统计量的猜想的集值扩展。这种双射还保留了排列中最大字母的邻居，从而解决了 Wang 和 Zhang 提出的 Spiro 猜想的改进。我们的分解可以扩展到标记良好的正路径，这是由多面体理论产生的一类广义选票排列，由 Bernardi、Duplantier 和 Nadeau 列举。

我们还将研究避免长度为 3 的单一模式的选票排列的枚举方面，并在避免 213 的选票排列和 Gessel walks 之间建立联系。