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Dickson–Stirling numbers

Published online by Cambridge University Press:  20 January 2009

L. C. Hsu ,
Gary L. Mullen  and
Peter Jau-Shyong Shiue
L. C. Hsu
Affiliation:
Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. of China
Gary L. Mullen
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.E-mail address:mullen@math.psu.edu
Peter Jau-Shyong Shiue
Affiliation:
Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV 89154-4020, U.S.A.E-mail address:shiue@nevada.edu
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Abstract

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The Dickson polynomial Dn, (x, a) of degree n is defined by 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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 409 - 423
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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