| 一类关于对称函数的卷积型求和公式 |
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| 引用本文： | 初文昌.一类关于对称函数的卷积型求和公式[J].大连理工大学学报,1986(3). |
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| 作者姓名： | 初文昌 |
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| 作者单位： | 大连工学院应用数学研究所 |
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| 摘 要： | 本文研究一类对称函数的卷积求和问题，利用交叉分类原理证明了所述问题的封闭性定理及其多重模拟。作为应用，文中给出了一系列有趣的推论。其中涉及二项系数、Ａｂｅｌ系数的卷积公式及其多重形式。这些结果包括 Ｗａｎｇ（１９６９），Ｃａｒｌｉｔｚ(１９７４）和 Ｓｉｎｇｈ Ｃｈａｎｄｅｌ＆Ｄｗｉｖｅｄｉ（１９７９）等人的著名恒等式作为特款。
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| 关 键 词： | 组合数学 二项式系数 卷积/对称函数 Abel系数 多项式系数 |
A Class of Summation Formulas Concerning Convolutions of Symmetric Functions |
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| Chu Wenchang Institute of Applied Mathematics,DIT.A Class of Summation Formulas Concerning Convolutions of Symmetric Functions[J].Journal of Dalian University of Technology,1986(3). |
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| Authors: | Chu Wenchang Institute of Applied Mathematics DIT |
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| Abstract: | This paper investigates convolutions with respect to symmetric functions. By using the pinciple of inclusion and exclusion, the author has obtained a general combinatorial identity concerning the above summation and its multifold analog. Several interesting consequences are given which are related to the convolutions of binomial and Abel coefficients and their multifold forms. Some famous identities of Wang, Carlitz and Singh Chandel& Dwivedi are included as their special cases. |
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| Keywords: | combinatorial mathematics binomial coefficient convolution/symm- etric function Abel coefficient multinomial coefficient |
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