Vector parking functions are sequences of non-negative integers whose order statistics are bounded by a given integer sequence $\mathbf{u}=(u_0,u_1,u_2,\dots )$. Using the theory of fractional power series and an analog of Newton-Puiseux Theorem, we derive the exponential generating function for the number of u-parking functions when u is periodic. Our method is to convert an Appell relation of Gončarov polynomials to a system of linear equations. Solving the system we obtain an explicit formula of the exponential generating function in terms of Schur functions of certain fractional power series. In particular, we apply our methods to rational parking functions for which the boundary is induced by a linear function with rational slope.

向量停放函数是非负整数的序列，其阶数统计受给定整数序列限制 $\mathbf{ü}=（{ü}_0，{ü}_{\mathrm{1个}}，{ü}_2，\dots ）$。利用分数阶幂级数理论和牛顿-普伊修斯定理的类似物，我们推导了当u为周期时，u-停车函数的数量的指数生成函数。我们的方法是将Gončarov多项式的Appell关系转换为线性方程组。求解该系统，我们可以根据某些分数次幂级数的Schur函数获得指数生成函数的显式公式。尤其是，我们将我们的方法应用于有理停车函数，其边界是由具有有理斜率的线性函数引起的。