论文标题
投票排列和奇数排列的托管特性
A Toeplitz property of ballot permutations and odd order permutations
论文作者
论文摘要
我们提供了一个新的半组合证明，以使长度$ n $的投票排列数量以及长度$ n $的奇数订单排列数量的平等，这是由于Bernardi，Duplantier和Nadeau所致。 Spiro的猜想认为，相同长度的奇数列表的投票排列数和某些循环重量是等式分布的。我们提出了一个两次射击，以建立具有任何固定数量下降数量的投票排列的Toeplitz属性，以及具有任何固定环状重量的奇数置换式托管属性。这使我们可以通过跟踪排列中最大字母的邻居来完善Spiro的猜想。
We give a new semi-combinatorial proof for the equality of the number of ballot permutations of length $n$ and the number of odd order permutations of length $n$, which is due to Bernardi, Duplantier and Nadeau. Spiro conjectures that the descent number of ballot permutations and certain cyclic weight of odd order permutations of the same length are equi-distributed. We present a bijection to establish a Toeplitz property for ballot permutations with any fixed number of descents, and a Toeplitz property for odd order permutations with any fixed cyclic weight. This allows us to refine Spiro's conjecture by tracking the neighbors of the largest letter in permutations.
