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Efficient Algorithms for Permutation Arrays from Permutation Polynomials [PDF]
EntropyWe develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields.
Sergey Bereg +3 more
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Permutations of massive vacua [PDF]
Journal of High Energy Physics, 2017 We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N $$ \mathcal{N} $$ = 1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N $$ \mathcal{N} $$ = 4 and N $$ \
Antoine Bourget, Jan Troost
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On permutation polynomials over finite fields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1987 A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a ...
R. A. Mollin, C. Small
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Tree snumeration polynomials on separable permutations
Enumerative Combinatorics and Applications, 2023 Summary: \textit{I. M. Pak} and \textit{A. E. Postnikov} [Russ. Math. Surv. 45, No. 3, 220--221 (1990; Zbl 0744.05020); translation from Usp. Mat. Nauk 45, No. 3(273), 193--194 (1990)] introduced a tree enumeration polynomial \(f_G\) on graphs, as a multivariate generalization of Cayley's formula, and demonstrated an amazing reciprocity property.
Yibo Gao, Siyu Liu
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Symplectic Spreads and Permutation Polynomials [PDF]
, 2004 Every symplectic spread of PG(3,q), or equivalently every ovoid of Q(4,q), is shown to give rise to a certain family of permutation polynomials of GF(q) and conversely. This leads to an algebraic proof of the existence of the Tits-Luneburg spread of W(2^{2h+1}) and the Ree-Tits spread of W(3^{2h+1}), as well as to a new family of low-degree permutation
Simeon Ball, Michael E. Zieve
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Inverses for Fourth-Degree Permutation Polynomials Modulo 32Ψ or 96Ψ, with Ψ as a Product of Different Prime Numbers Greater than Three [PDF]
AppliedMathIn this paper, we address the inverse of a true fourth-degree permutation polynomial (4-PP), modulo a positive integer of the form 32kLΨ, where kL∈{1,3} and Ψ is a product of different prime numbers greater than three. Some constraints are considered for
Lucian Trifina +2 more
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Research Progress on Permutation Polynomials in Finite Fields [PDF]
Jisuanji gongcheng, 2019 The Akbary-Ghioca-Wang(AGW) criterion and piecewise method are two main methods for constructing permutation polynomials of finite fields.This paper introduces the application of permutation polynomials in cryptography and coding theory,reviews the ...
ZHENG Yanbin, YI Zongxiang
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Quasi-permutation polynomials [PDF]
Czechoslovak Mathematical Journal, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Laohakosol, Vichian +1 more
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Permutation polynomials and group permutation polynomials [PDF]
Bulletin of the Australian Mathematical Society, 2001 Permutation polynomials of the form xτf (x3) over a finite field give rise to group permutation polynomials. We give a group theoretic criterion and some other criteria in terms of symmetric functions and power functions.
Park, Young Ho, Lee, June Bok
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A Class of New Permutation Polynomials over F2n
Journal of Mathematics, 2021 In this paper, according to the known results of some normalized permutation polynomials with degree 5 over F2n, we determine sufficient and necessary conditions on the coefficients b1,b2∈F2n2 such that fx=x3x¯2+b1x2x¯+b2x permutes F2n.
Qian Liu, Ximeng Liu, Jian Zou
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