## On the Carlitz rank of permutation polynomials
Aksoy, Esen and Çeşmelioğlu, Ayça and Meidl, Wilfried and Topuzoğlu, Alev (2009)
Full text not available from this repository. Official URL: http://dx.doi.org/10.1016/j.ffa.2009.02.006 ## AbstractA well-known result of Carlitz, that any permutation polynomial p(x) of a finite field F-q is a composition of linear polynomials and the monomial x(q-2). implies that V(x) can be represented by a polynomial P-n(x) = (...((a(0)x + a(1))(q-2) + a(2))(q-2)...+ a(n))(q-2) + a(n+1). for some n >= 0. The smallest integer n, such that P,,(x) represents p(x) is of interest since it is the least number of "inversions" x(q-2), needed to obtain p(x). We define the Carlitzrank of p(x) as n, and focus here on the problem of evaluating it. We also obtain results on the enumeration of permutations of F-q with a fixed Carlitz rank.
## Available Versions of this Item- On the Carlitz rank of permutation polynomials. (deposited 27 May 2009 11:45)
- On the Carlitz rank of permutation polynomials. (deposited 03 Dec 2009 16:48)
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- On the Carlitz rank of permutation polynomials. (deposited 03 Dec 2009 16:48)
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