2003/10/31 by Frédéric Chyzak, Marni Mishna, Bruno Salvy · 1 citation
Mathematics · #math.CO #msc:05E05 #msc:05A16 #msc:05A15
paper · pdf · doi:10.1016/j.jcta.2005.01.001
published as Journal of Combinatorial Theory Series A, Volume 112 , Issue 1 (October 2005), Pages: 1 - 43 · 51 pages, full paper version of FPSAC 02 extended abstract; v2: corrections from original submission, improved clarity; now formatted for journal + bibliography
arxiv created 2012/11/13 · arxiv updated 2012/11/14
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.