Dickson-stirling numbers

L. C. Hsu, Gary Lee Mullen, Peter Jau Shyong Shiue

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)409-423
Number of pages15
JournalProceedings of the Edinburgh Mathematical Society
Volume40
Issue number3
StatePublished - Dec 1 1997

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Dickson Polynomials
Stirling numbers
Stirling numbers of the first kind
Stirling numbers of the second kind
Enumeration
Finite Set
Denote
Range of data

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Hsu, L. C. ; Mullen, Gary Lee ; Shiue, Peter Jau Shyong. / Dickson-stirling numbers. In: Proceedings of the Edinburgh Mathematical Society. 1997 ; Vol. 40, No. 3. pp. 409-423.
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Hsu, LC, Mullen, GL & Shiue, PJS 1997, 'Dickson-stirling numbers', 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.

In: Proceedings of the Edinburgh Mathematical Society, Vol. 40, No. 3, 01.12.1997, p. 409-423.

Research output: Contribution to journalArticle

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