Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
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Oleg A. Kozlitin
Abstract
The paper is concerned with polynomial transformations of a finite commutative local principal ideal of a ring (a finite commutative uniserial ring, a Galois–Eisenstein ring). It is shown that in the class of Galois–Eisenstein rings with equal cardinalities and nilpotency indexes over Galois rings there exist polynomial generators for which the period of the output sequence exceeds those of the output sequences of polynomial generators over other rings.
Originally published in Diskretnaya Matematika (2017) 29,№4, 41–58 (in Russian).
Acknowledgment
The author is indebted to P. V. Roldugin for pertinent remarks concerning this manuscript. The author dedicates this paper to the memory of A. A. Nechaev.
References
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Articles in the same Issue
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
Articles in the same Issue
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
