Effective scalar products of D-finite symmetric functions

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• 作者：Fré ; dé ; ric Chyzak ; Marni Mishna and Bruno Salvy
• 关键词：Symmetric functions ; Differentiably finite functions ; Non-commutative Groebner bases ; Hammond series ; Holonomic D-modules ; Kronecker products ; Regular graphs ; Uniform Young tableaux
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：112
• 期：1
• 页码：1-43
• 全文大小：461 K

文摘

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.