Counting and Computing by $e$

Mehdi Hassani

Counting and Computing by $e$

组合数学 2007-05-23 v1 数论

作者: Mehdi Hassani

摘要

In this paper we count the number of paths and cycles in complete graphs by using the number $e$ . Also, we compute the number of derangements in same way. Connection by $e$ yields some nice formulas for the number of derangements, such as $D_n=\lfloor\frac{n!+1}{e}\rfloor$ and $D_n=\lfloor(e+e^{-1})n!\rfloor-\lfloor en!\rfloor$ , and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; these connections are hidden in the heart of a nice polynomial that we call it derangement function and a simple ordinary differential equation concerning it.

关键词

graph theory graph cycles dyck paths

引用

@article{arxiv.math/0606613,
  title  = {Counting and Computing by $e$},
  author = {Mehdi Hassani},
  journal= {arXiv preprint arXiv:math/0606613},
  year   = {2007}
}

备注

12 pages, no figure, review of my works about the number of derangements

Counting and Computing by $e$

摘要

关键词

引用

备注

相关论文