D-有限对称函数的有效标量积
Effective Scalar Products for D-finite Symmetric Functions
摘要：
许多组合生成函数可以表示为对称函数的组合，或者从这样的组合中提取子序列和特化。Gessel概述了一大类对称函数，其生成函数是D-有限的。我们扩展Gessel的工作，提供算法，计算微分方程这些生成函数满足的情况下，他们给出了作为一个标量产品的对称函数Gessel的类。最后给出了k-正则图和具有重复项的Young表的应用实例。渐近估计是我们的方法的自然应用，我们说明了相同的模型的Young tableaux。我们还得到了一个看似新的公式的克罗内克积的Schur函数的和与自身。
英文摘要：
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the resulting generating functions are D-finite. We extend Gessel's work by providing algorithms that compute differential equations these generating functions satisfy in the case they are given as a scalar product of symmetric functions in Gessel's class. Examples of applications to k-regular graphs and Young tableaux with repeated entries are given. Asymptotic estimates are a natural application of our method, which we illustrate on the same model of Young tableaux. We also derive a seemingly new formula for the Kronecker product of the sum of Schur functions with itself.
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