FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 1, PAGES 113-148

Hopf algebras of linear recurring sequences over rings and modules

V. L. Kurakin

Abstract

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The module of linear recurring sequences over a commutative ring $R$ can be considered as a Hopf algebra dual to the polynomial Hopf algebra over $R$. Under this approach, some notions and operations from the Hopf algebra theory have an interesting interpretation in terms of linear recurring sequences. Generalizations are also considered: linear recurring bisequences, sequences over modules, and $k$-sequences.

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Last modified: April 4, 2004.