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A Low-Order Permutationally Invariant Polynomial Approach to Learning Potential Energy Surfaces Using the Bond-Order Charge-Density Matrix: Application to C_n Clusters for n = 3-10, 20. [PDF]

J Phys Chem A
Gutierrez-Cardenas J, Gibbas BD, Whitaker K, Kaledin M, Kaledin AL.   +4 more
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Constructing permutation polynomials from permutation polynomials of subfields

Finite Fields and Their Applications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lucas Reis, Qiang Wang
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Permutation polynomials and factorization

Cryptography and Communications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kalaycı, Tekgül, Stichtenoth, Henning, Topuzoğlu, Alev   +2 more
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Testing permutation polynomials

30th Annual Symposium on Foundations of Computer Science, 1989
The simple test for determining whether an arbitrary polynomial is a permutation polynomial, by producing its list of values, is considered, and it is found that off-the-shelf techniques from computer algebra improve the running time slightly, without requiring any new insights into the problem.
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Permutation polynomials and primitive permutation groups

Archiv der Mathematik, 1991
In 1966 L. Carlitz conjectured that for every even positive integer \(n\) there exists a constant \(c_ n\) such that for any odd \(q>c_ n\) there is no permutation polynomial of degree \(n\) over the finite field \(F_ q\) of order \(q\). This conjecture was known to hold for \(n\) a power of 2 and for all even \(n\leq 16\). In this paper the conjecture
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Linear Permutation Polynomial Codes

2019 IEEE International Symposium on Information Theory (ISIT), 2019
Quasi-cyclic low-density parity-check (QC-LDPC) codes are one of the most important code classes of LDPC codes. They have two drawbacks: lack of randomness and limited girth lead to a degraded decoding performance in the waterfall and error floor regions, respectively.
Ryoichiro Yoshida, Kenta Kasai
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Witt Rings and Permutation Polynomials

Algebra Colloquium, 2005
Let p be a prime number. In this paper, the author sets up a canonical correspondence between polynomial functions over ℤ/p2ℤ and 3-tuples of polynomial functions over ℤ/pℤ. Based on this correspondence, he proves and reproves some fundamental results on permutation polynomials mod pl.
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ON SOME CLASSES OF PERMUTATION POLYNOMIALS

International Journal of Number Theory, 2008
Let p be a prime and q = pm. We investigate permutation properties of polynomials P(x) = xr + xr+s + ⋯ + xr+ks (0 < r < q - 1, 0 < s < q - 1, and k ≥ 0) over a finite field 𝔽q. More specifically, we construct several classes of permutation polynomials of this form over 𝔽q. We also count the number of permutation polynomials in each class.
Akbary, Amir, Alaric, Sean, Wang, Qiang
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Tests for Permutation Polynomials

SIAM Journal on Computing, 1991
If $\mathbb{F}_q $ is a finite field and $f \in \mathbb{F}_q [x]$, then f is called a permutation polynomial if the mapping $\mathbb{F}_q \to \mathbb{F}_q $ induced by f is bijective. This property can be tested by a probabilistic algorithm whose number of operations is polynomial (in fact, essentially linear) in the input size, i.e., in $\deg f \cdot \
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