论文标题
部分偏斜Motzkin路径
Partial Skew Motzkin Paths
论文作者
论文摘要
Motzkin路径由上步，下台，级别步骤组成，并且永远不会低于$ x $轴。他们最后返回到$ x $轴。偏斜的dyck路径\ cite {deutsch-titery}的概念被转移到偏斜的motzkin路径上，即，左步$（-1，-1）$也是允许的，但不允许该路径与本身相交。这些组合对象的枚举已知\ cite {qing};在这里，使用内核方法，我们通过允许它们以规定的级别$ j $结束来扩展结果。该方法完全基于生成功能。 还给出了对象总数以及平均高度的渐近学。
Motzkin paths consist of up-steps, down-steps, level-steps, and never go below the $x$-axis. They return to the $x$-axis at the end. The concept of skew Dyck path \cite{Deutsch-italy} is transferred to skew Motzkin paths, namely, a left step $(-1,-1)$ is additionally allowed, but the path is not allowed to intersect itself. The enumeration of these combinatorial objects was known \cite{Qing}; here, using the kernel method, we extend the results by allowing them to end at a prescribed level $j$. The approach is completely based on generating functions. Asymptotics of the total number of objects as well as the average height are also given.
