@article{CHYZAK20051,
    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.},
    Author = {Chyzak, Fr{\'e}d{\'e}ric and Mishna, Marni and Salvy, Bruno},
    File = {Effective scalar products of D-finite symmetric functions - 1-s2.0-S0097316505000087-main - a.pdf},
    ISSN = {0097-3165},
    Journal = {Journal of Combinatorial Theory, Series A},
    Keywords = {Symmetric functions, Differentiably finite functions, Non-commutative Groebner bases, Hammond series, Holonomic D-modules, Kronecker products, Regular graphs, Uniform Young tableaux},
    Number = {1},
    Pages = {1-43},
    Title = {Effective scalar products of D-finite symmetric functions},
    URL = {https://www.sciencedirect.com/science/article/pii/S0097316505000087},
    Volume = {112},
    Year = {2005},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0097316505000087},
    bdsk-url-2 = {https://doi.org/10.1016/j.jcta.2005.01.001},
    date-added = {2023-03-13 07:45:06 +0100},
    date-modified = {2023-03-13 07:45:06 +0100},
    doi = {10.1016/j.jcta.2005.01.001}
}

@article{CHYZAK20051, 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.}, Author = {Chyzak, Fr{\'e}d{\'e}ric and Mishna, Marni and Salvy, Bruno}, File = {Effective scalar products of D-finite symmetric functions - 1-s2.0-S0097316505000087-main - a.pdf}, ISSN = {0097-3165}, Journal = {Journal of Combinatorial Theory, Series A}, Keywords = {Symmetric functions, Differentiably finite functions, Non-commutative Groebner bases, Hammond series, Holonomic D-modules, Kronecker products, Regular graphs, Uniform Young tableaux}, Number = {1}, Pages = {1-43}, Title = {Effective scalar products of D-finite symmetric functions}, URL = {https://www.sciencedirect.com/science/article/pii/S0097316505000087}, Volume = {112}, Year = {2005}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0097316505000087}, bdsk-url-2 = {https://doi.org/10.1016/j.jcta.2005.01.001}, date-added = {2023-03-13 07:45:06 +0100}, date-modified = {2023-03-13 07:45:06 +0100}, doi = {10.1016/j.jcta.2005.01.001} }