Transformation formulas for complete symmetric polynomials and identities for generalized binomial coefficients and -Stirling numbers

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• 作者：Luis Verde-Star ^{verde@xanum.uam.mx}
• 关键词：Symmetric polynomials ; Gaussian coefficients ; Generalized Stirling numbers ; q-Stirling numbers ; Legendre&ndash ; Stirling numbers
• 刊名：Discrete Mathematics
• 出版年：2012
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：6 August, 2012
• 卷：312
• 期：15
• 页码：2197-2202
• 文件大小：212 K

摘要

We obtain explicit formulas that express the complete homogeneous symmetric polynomials of the sequence of partial sums of a sequence as polynomials in the , and conversely, the complete homogeneous symmetric polynomials of the as polynomials in the . Taking particular sequences , we obtain combinatorial identities for several types of generalized binomial coefficients, including Gaussian coefficients, Stirling numbers of the second kind, -Stirling numbers of the second kind, and Legendre-Stirling numbers. We also introduce some new families of generalized binomial coefficients and Stirling numbers.