k-色斜Dyck路的计数

Enumeration of k-colored skew Dyck path

本文研究k-色斜Dyck路的计数问题,给出半长为n的k-色斜Dyck路的数目s_n的计数公式、递推关系以及s_n/s_(n-1)的极限,并对半长、左步数、峰数、谷数以及双升数等参数给出了k-色斜Dyck路相应的计数公式.

In this paper we study the enumeration of k-colored skew Dyck paths.We first give a counting formula and a recurrence for s_n and the limit of s_n/s_（n-1）.We then give the counting formulas of the k-colored skew Dyck paths with semilength n according to the number of left steps and the number of peaks,valleys and double rises.