Combinatorial interpretation of integrals of products of hermite, Laguerre and Tchebycheff polynomials
Combinatorial interpretation of integrals of products of hermite, Laguerre and Tchebycheff polynomials
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Hermite、Laguerre 和 Tchebycheff 多项式乘积积分的组合解释
DOI：
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
G. Viennot
中科院分区：
文献类型：
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作者：
M. D. Sainte;G. Viennot
laaguerre多项式积的某些积分已经被Kaplansky、Even、Gillis、Jackson、Askey、Ismail和Rashed解释为广义无序的数。Azor, Gillis, Victor， Godsil在匹配方面对Hermite多项式做了类似的研究。这里我们给出这些结果的一个简单的组合证明（即双射证明）。对于切比切夫多项式的情况，构造了一个类似的双射，并导致了戴克词的解释。
Certain integrals of products of Laguerre polynomials have been interpreted as numbers of generalized derangements by Kaplansky, Even, Gillis, Jackson, Askey, Ismail, and Rashed. The analog for the Hermite polynomials have been done by Azor, Gillis, Victor, Godsil in term of matchings. Here we give a simple combinatorial (i.e. with a bijection) proof of these results. An analogous bijection is constructed for the case of Tchebycheff polynomials and leads to an interpretation with Dyck words.