有限域上线性递归序列簇及其周期性(英文)ON PERIODICITY AND FAMILIY OF LINEARLY RECURSIVE SEQUENCES OVER FINITE FIELDS
潘庆年
摘要(Abstract):
本文首次使用了HOPF代数的方法,研究了有限域F_q上线性递归序列问题,主要的结果如下:(1)有限域F_q上每一个线性递归序列都是终归周期的(ultimatelyperiodic).(2)S(f(x))=(f(x)).此外,我们还推广和化简了[5]中许多工作。你将发现这种方法比较方便、自然,而且值得进一步探讨。
关键词(KeyWords): 线性递归序列;连续对偶代数;Hopf代数
基金项目(Foundation):
作者(Author): 潘庆年
DOI: 10.16778/j.cnki.1671-5934.1997.04.007
参考文献(References):
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- [2] E. J. Taft, Hurwitz invertiblity of linearly recursive sequences, Congressus Numerantium, Vol, 73(1990), 37-40.
- [3] R. Larson and E. J. Taft. The Hopf Structure of Linearly Recursive Sequences under Hardamard Product,(preprint 1990, to appear in Isreal J. Mathematics)
- [4] M. E. Sweedler. Hopf Algebras, Benjamin, New York (1969).
- [5] R. Lidl & H. Niederreiter, Finite Fields, Ency. of Math. and its appl. Vol. 20. Addison-wesley (1983).