Effective scalar products of D-finite symmetric functions |
| |
Authors: | Frédéric Chyzak |
| |
Institution: | a Projet Algorithmes, INRIA Rocquencourt, France b LaCIM, Dépt. de Mathématiques Université du Québec à Montréal CP 8888, succ. Centre-ville Montréal, QC, Canada H2X 3Y7 |
| |
Abstract: | 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. |
| |
Keywords: | 05E05 05E10 13N10 13P10 |
本文献已被 ScienceDirect 等数据库收录! |
|