### 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) |
---|---|

Pages (from-to) | 409-423 |

Number of pages | 15 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 40 |

Issue number | 3 |

State | Published - Dec 1 1997 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*40*(3), 409-423.

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*Proceedings of the Edinburgh Mathematical Society*, vol. 40, no. 3, pp. 409-423.

**Dickson-stirling numbers.** / Hsu, L. C.; Mullen, Gary Lee; Shiue, Peter Jau Shyong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dickson-stirling numbers

AU - Hsu, L. C.

AU - Mullen, Gary Lee

AU - Shiue, Peter Jau Shyong

PY - 1997/12/1

Y1 - 1997/12/1

N2 - The Dickson polynomial Dn (x, a) of degree n is defined by Dn (x, a) = ∑i=0[n/2] n/n-i (in-i) (-a)i xn-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D0 (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.

AB - The Dickson polynomial Dn (x, a) of degree n is defined by Dn (x, a) = ∑i=0[n/2] n/n-i (in-i) (-a)i xn-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D0 (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.

UR - http://www.scopus.com/inward/record.url?scp=21944439071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21944439071&partnerID=8YFLogxK

M3 - Article

VL - 40

SP - 409

EP - 423

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -