解多元函数方程
Solving multivariate functional equations
摘要：
本文提出了一种求解多元母函数的函数方程的新方法，如$$F(r,s)=e(r,s)+xf(r,s)F(1,1)+xg(r,s)F(qr,1)+xh(r,s)F(qr,qs),$$给出了$F(r,s)$在有限序列上求和的公式。我们用这种方法来说明如何计算的系数的生成函数的多角形，这是不切实际的使用其他方法。我们也应用这种方法来回答一个问题，从完全交换仿射置换。
英文摘要：
This paper presents a new method to solve functional equations of multivariate generating functions, such as $$F(r,s)=e(r,s)+xf(r,s)F(1,1)+xg(r,s)F(qr,1)+xh(r,s)F(qr,qs),$$ giving a formula for $F(r,s)$ in terms of a sum over finite sequences. We use this method to show how one would calculate the coefficients of the generating function for parallelogram polyominoes, which is impractical using other methods. We also apply this method to answer a question from fully commutative affine permutations.
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