How to Cite
Downloads
Most read articles by the same author(s)
- Pablo A. Acosta-Solarte, Víctor S. Albis, PERMUTATION POLYNOMIALS IN ONE INDETERMINATE OVER MODULAR ALGEBRAS , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 30 No. 117 (2006)
- Víctor S. Albis, Deisy Y. Camargo, PEDRO J. SOSA, A GREAT MATHEMATICAL ENGINEER , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 29 No. 113 (2005)
Métricas Alternativas
Dimensions
Abstract
Known results about permutation polynomials in connection with coefficients in a finite field extend to algebras of the form Lv = K[X]/(p(X)v)\), where K is a finite field,(p(X) ∈ K[X] is an irreducible polynomial, and v = 1,2,..., and to the algebra of power series L[[Z]], where L = K[X]/(p(X)). Analogues of Dickson polynomials are also studied in this context.
Keywords
References
Albís, V. S. Iterative Methods for Some Problems of Matrix Algebra. Matemáticas 22 (2001), 3-15.
Albís, V. S., & Osuna, R. On a Conjugate Gradient Algorithm for Inversion of Block Tridiagonal Matrices. Rev. Acad. Colomb. Cienc. 25 (2001), 163-179. [MR: 1860.65107]
Daqing, V. Perturbation Analysis for a Singular Linear System over Finite Fields. Adv. Math. Sci. Appl. 10 (2000), 345-355. [MR: 1796998]
Dickson, L. J. C. Linear Groups: With an Exposition of the Galois Field Theory. Dover Publications, New York, 1958.
Friese, M. On a Conjecture of Schur. Michigan Math. J. 14 (1967), 41-53. [MR: 41:5968]
Greenberg, M. J. Lectures on Forms of Many Variables. W. A. Benjamin, New York, 1969.
Lidl, R., & Lidl, N. Permutations as Polynomials over a Finite Field. Aequationes Math. 35 (1988), 243-246.
Lidl, R., & Niederreiter, H. Finite Fields. Encyclopedia of Mathematics and Its Applications, Addison-Wesley Publishing Company, Reading, Mass., 1983. [MR: 85h:11100]
McDonald, B. R. Finite Rings with Identity. Marcel Dekker, New York, 1974.
Smits, T. H. "On the Group of Permutations in GF(q) over X ↦→ X^u/(X^v - X)." Indag. Math. 44 (1982), 355-368.
Sun, Q. "A Note on Permutation Polynomials over Finite Fields." Sci. China Ser. A 21, No. 1 (1978), 111-116. [Translated from Chinese: Scientia Sinica, Vol. 21, No. 1 (1978), 1-8.]
Zhuang, Q. "On Permutations in Several Finite Fields Which Are Transformable to Permutation Polynomials of the Type (X^u - X^v)." Adv. Math. 22, No. 6 (1993), 456-457.
Zhang, Q. "Permutation Polynomials in Several Finite Fields." Chinese Ann. Math. Ser. A 16, No. 2 (1995), 165-176. [Original Chinese: 数学学报, Vol. 38, No. 2 (1995), 1-12.]
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2023 https://creativecommons.org/licenses/by-nc-nd/4.0