Generalized Vandermonde determinants and characterization of divisibility sequences

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• 作者：Stefano Barbero ^{stefano.barbero@unito.it}
• 关键词：11B37 ; 11B83
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：173
• 期：Complete
• 页码：371-377
• 全文大小：226 K
• 卷排序：173

文摘

We present a different proof of the characterization of non-degenerate linear recurrence sequences, which are also divisibility sequences, given by Van der Poorten, Bézivin, and Pethö in their paper “A Full Characterization of Divisibility Sequences” [1]. Our proof is based on an interesting determinant identity, related to impulse sequences, obtained from the evaluation of a generalized Vandermonde determinant. As a consequence of this new proof we can find a more precise form for the resultant sequence presented in [1], in the general case of non-degenerate divisibility sequences having minimal polynomial with multiple roots.