### Abstract

The Dickson polynomial D_{n} (x, a) of degree n is defined by D_{n} (x, a) = ∑_{i=0}^{[n/2]} n/n-i (_{i}^{n-i}) (-a)^{i} x^{n-21}, where ⌊⌋ denotes the greatest integer function. In particular, we define D_{0} (x, a) = 2 for all real x and a. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.

Original language | English (US) |
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Pages (from-to) | 409-423 |

Number of pages | 15 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 40 |

Issue number | 3 |

DOIs | |

State | Published - 1997 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Hsu, L. C., Mullen, G. L., & Shiue, P. J. S. (1997). Dickson-stirling numbers.

*Proceedings of the Edinburgh Mathematical Society*,*40*(3), 409-423. https://doi.org/10.1017/s0013091500023919