| Two Kinds of Numbers and Their Applications |
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| 作者姓名： | Zhi Zheng ZHANG Hong FENG |
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| 作者单位： | [1]Department of Mathematics, Luoyang Teachers＇ College, Luoyang 471022, P. R. China [2]College of Mathematics and Information Science, Henan University, Kaifeng 475001, P. R. China [3]Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China |
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| 基金项目： | This research is supported by the National Natural Science Foundation of China （Grant No. 10471016）, the Natural Science Foundation of Henan Province （Grant No. 0511010300） and the Natural Science Foundation of the Education Department of Henan Province （Grant No. 200510482001） Acknowledgements The authors would like to thank the anonymous referee for many valuable suggestions. |
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| 摘 要： | C. Radoux （J. Comput. Appl. Math., 115 （2000） 471-477） obtained a computational formula of Hankel determinants on some classical combinatorial sequences such as Catalan numbers and polynomials, Bell polynomials, Hermite polynomials, Derangement polynomials etc. From a pair of matrices this paper introduces two kinds of numbers. Using the first kind of numbers we give a unified treatment of Hankel determinants on those sequences, i.e., to consider a general representation of Hankel matrices on the first kind of numbers. It is interesting that the Hankel determinant of the first kind of numbers has a close relation that of the second kind of numbers.
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| 关 键 词： | 组合序列 Hankel行列式 组合识别 Hermite多项式 |
| 收稿时间： | 2005-01-18 |
| 修稿时间： | 2005-01-182005-05-31 |
Two Kinds of Numbers and Their Applications |
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| Zhi Zheng ZHANG Hong FENG.Two Kinds of Numbers and Their Applications[J].Acta Mathematica Sinica,2006,22(4):999-1006. |
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| Authors: | Zhi Zheng Zhang Hong Feng |
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| Institution: | (1) Department of Mathematics, Luoyang Teachers’ College, Luoyang 471022, P. R. China;(2) College of Mathematics and Information Science, Henan University, Kaifeng 475001, P. R. China;(3) Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China |
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| Abstract: | C. Radoux (J. Comput. Appl. Math.
115 (2000) 471–477) obtained a computational formula of Hankel determinants on some classical combinatorial sequences such as
Catalan numbers and polynomials, Bell polynomials, Hermite polynomials, Derangement polynomials etc. From a pair of matrices
this paper introduces two kinds of numbers. Using the first kind of numbers we give a unified treatment of Hankel determinants
on those sequences, i.e., to consider a general representation of Hankel matrices on the first kind of numbers. It is interesting
that the Hankel determinant of the first kind of numbers has a close relation that of the second kind of numbers.
This research is supported by the National Natural Science Foundation of China (Grant No. 10471016), the Natural Science Foundation
of Henan Province (Grant No. 0511010300) and the Natural Science Foundation of the Education Department of Henan Province
(Grant No. 200510482001) |
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| Keywords: | combinatorial sequence Hankel determinant combinatorial identity |
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