Enumeration of symplectic and orthogonal injective partial transformations

@article{Li2006EnumerationOS,
  title={Enumeration of symplectic and orthogonal injective partial transformations},
  author={Zhenheng Li and Zhuo Zhe Li and You'an Cao},
  journal={Discrete Mathematics},
  year={2006},
  volume={306},
  pages={1781-1787}
}
In this paper, we compute the generating function of sn =∑ni=0 ai(ni )2i!, where a is a real number with a ≥ 1. We then use this function to determine the generating functions of the symplectic and orthogonal Renner monoids. Furthermore, we show that these functions are closely related to Laguerre polynomials. © 2006 Elsevier B.V. All rights reserved.