Effective scalar products of D-finite symmetric functions
نویسندگان
چکیده
منابع مشابه
Effective scalar products of D-finite symmetric functions
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 sa...
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Many enumerative problems can be expressed using the scalar product of symmetric functions. As we shall see, we can set up expressions for the generating functions of objects which possess a certain kind of regularity as a scalar product. Two examples of this are k-regular graphs (graphs in which each vertex is of degree k), and secondly we have a class of semi-standard Young tableaux in which ...
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The fruitful relation between the theory of symmetric functions and that of D-finite power series was first introduced by Goulden and Jackson in 1980, and later extended by Gessel, who stated two important results that provide closure properties of D-finite symmetric series under the scalar and inner products. These products are very important from the computational and combinatorial points of ...
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Using an algorithm for computing the symmetric function Kronecker product of D-finite symmetric functions we find some new Kronecker product identities. The identities give closed form formulas for trace-like values of the Kronecker product. Introduction In the process of showing how the scalar product of symmetric functions can be used for enumeration purposes, Gessel [3], proved that this pro...
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The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. The algorithm consists essentially of Gauss’ upper triangular form algorithm. It is proved that the basis of the ideal of algebraic relations found by the algorithm consists of polynomials having coefficie...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.01.001