论文标题
峰值高度的分布Modulo $ k $和$ k $ -dock路径上的双重下降
Distribution of peak heights modulo $k$ and double descents on $k$-Dyck paths
论文作者
论文摘要
我们表明，给定长度的高度$ i $ modulo $ k $在$ k $ -dyck路径中的峰值分布独立于[0，k-1] $中的$ i \，并且是峰值总数的分布的逆转。此外，这些统计数据以及双重下降的数量与它们的任何排列共同等分。我们还将这一结果推广到广义的Motzkin路径和广义投票路径。
We show that the distribution of the number of peaks at height $i$ modulo $k$ in $k$-Dyck paths of a given length is independent of $i\in[0,k-1]$ and is the reversal of the distribution of the total number of peaks. Moreover, these statistics, together with the number of double descents, are jointly equidistributed with any of their permutations. We also generalize this result to generalized Motzkin paths and generalized ballot paths.
