Dickson-stirling numbers

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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
Issue number3
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • General Mathematics


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