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International Journal of Mathematics and Mathematical Sciences, 1990 A polynomial f over a finite feld F is a permutation polynomial if the mapping F→F defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j≥1.
Charles Small
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Permutations from APN power functions over F22n
网络与信息安全学报, 2017 APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over F22n.By generalizing the idea of changing 2-1 functions to ...
Shi-zhu TIAN
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Uniform estimates for smooth polynomials over finite fields
Discrete Analysis, 2023 Uniform estimates for smooth polynomials over finite fields, Discrete Analysis 2023:16, 31 pp. A positive integer $n$ is called $m$-_smooth_ if its largest prime factor has size at most $m$.
Ofir Gorodetsky
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Some identities on derangement and degenerate derangement polynomials
, 2017 In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number.
AM Garsia +14 more
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Enumerating Permutation Polynomials I: Permutations with Non-Maximal Degree
Finite Fields and Their Applications, 2002 Every permutation \(\sigma\) on the elements of \(\mathbb F_q\) (\(q>2\)) is uniquely represented by a polynomial \(f_\sigma\in\mathbb F_q[x]\) of degree \(\leq q-2\). A lower bound for the degree of \(f_\sigma\) is given by the number of fixed points of \(\sigma\) (\(\sigma\not=\text{id}\)).
MALVENUTO C, PAPPALARDI, FRANCESCO
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Invariant and polynomial identities for higher rank matrices
, 2007 We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank.
Asanov G S +15 more
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Complete permutation polynomials from exceptional polynomials
Journal of Number Theory, 2017 We classify complete permutation polynomials of type $aX^{\frac{q^n-1}{q-1}+1}$ over the finite field with $q^n$ elements, for $n+1$ a prime and $n^4 < q$. For the case $n+1$ a power of the characteristic we study some known families. We also classify indecomposable exceptional polynomials of degree $8$ and $9$.
D. Bartoli +3 more
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Product of Stanley symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We study the problem of expanding the product of two Stanley symmetric functions $F_w·F_u$ into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial $F_w=\lim _n ...
Nan Li
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Permutation Polynomials Modulo 2w
Finite Fields and Their Applications, 2001 The author explicitly characterizes permutation polynomials modulo \(2^n\) for \(n\geq 2\). In addition, he proves that pairs of polynomials defining a pair of orthogonal Latin squares (modulo \(2^n\)) do not exist.
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About permutations on the sets of tuples from elements of the finite field
Учёные записки Казанского университета: Серия Физико-математические науки, 2019 The following problem was considered: let S = S1× S2×…× Sm be the Cartesian product of subsets Si that are subgroups of the multiplicative group of a finite field Fq of q elements or their extensions by adding a zero element; a map f: S→ S of S into ...
V.S. Kugurakov +2 more
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