Henry W. GOULD,何天晓.Characterization of $(c)$Riordan Arrays, GegenbauerHumbertType Polynomial Sequences, and $(c)$Bell Polynomials[J].数学研究及应用,2013,33(5):505~527 
Characterization of $(c)$Riordan Arrays, GegenbauerHumbertType Polynomial Sequences, and $(c)$Bell Polynomials 
Characterization of $(c)$Riordan Arrays, GegenbauerHumbertType Polynomial Sequences, and $(c)$Bell Polynomials 
投稿时间：20121207 修订日期：20130218 
DOI：10.3770/j.issn:20952651.2013.05.001 
中文关键词: Riordan arrays $(c)$Riordan arrays $A$sequence $Z$sequence $(c)$Bell polynomials $(c)$hittingtime subgroup. 
英文关键词:Riordan arrays $(c)$Riordan arrays $A$sequence $Z$sequence $(c)$Bell polynomials $(c)$hittingtime subgroup. 
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中文摘要: 
Here presented are the definitions of $(c)$Riordan arrays and $(c)$Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of $(c)$Riordan arrays by means of the $A$ and $Z$sequences is given, which corresponds to a horizontal construction of a $(c)$Riordan array rather than its definition approach through column generating functions. There exists a onetoone correspondence between GegenbauerHumberttype polynomial sequences and the set of $(c)$Riordan arrays, which generates the sequence characterization of GegenbauerHumberttype polynomial sequences. The sequence characterization is applied to construct readily a $(c)$Riordan array. In addition, subgrouping of $(c)$Riordan arrays by using the characterizations is discussed. The $(c)$Bell polynomials and its identities by means of convolution families are also studied. Finally, the characterization of $(c)$Riordan arrays in terms of the convolution families and $(c)$Bell polynomials is presented. 
英文摘要: 
Here presented are the definitions of $(c)$Riordan arrays and $(c)$Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of $(c)$Riordan arrays by means of the $A$ and $Z$sequences is given, which corresponds to a horizontal construction of a $(c)$Riordan array rather than its definition approach through column generating functions. There exists a onetoone correspondence between GegenbauerHumberttype polynomial sequences and the set of $(c)$Riordan arrays, which generates the sequence characterization of GegenbauerHumberttype polynomial sequences. The sequence characterization is applied to construct readily a $(c)$Riordan array. In addition, subgrouping of $(c)$Riordan arrays by using the characterizations is discussed. The $(c)$Bell polynomials and its identities by means of convolution families are also studied. Finally, the characterization of $(c)$Riordan arrays in terms of the convolution families and $(c)$Bell polynomials is presented. 
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