A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials

作者：Ismail Mourad E H; Zeng Jiang^*

来源：Advances in Applied Mathematics, 2015, 64: 70-88.

DOI：10.1016/j.aam.2014.12.002

• 2D-Hermite polynomials
• 2D-Laguerre polynomials
• Kibble-Slepian formula
• Linearization coefficients
• Elementary symmetric functions
• Inequalities
• Positivity
• Shifted Laguerre polynomials

The first author has recently proved a Kibble-Slepian type formula for the 2D-Hermite polynomials {H-m,H- n(z, (z) over bar)} which extends the Poisson kernel for these polynomials. We provide a combinatorial proof of a closely related formula. The combinatorial structures involved are the so-called m-involutionary l-graphs. They are enumerated in two different manners: first globally, then as the exponential of their connected components. We also give a combinatorial model for the 2D-Laguerre polynomials and study their linearization coefficients.

• 出版日期2015-3