The Carlitz rank of permutations of finite fields: a survey
Topuzoğlu, Alev (2014) The Carlitz rank of permutations of finite fields: a survey. Journal of Symbolic Computation (SI), 64 . pp. 53-66. ISSN 0747-7171
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Official URL: http://dx.doi.org/10.1016/j.jsc.2013.07.004
L. Carlitz proved that any permutation polynomial f of a finite field Fq is a composition of linear polynomials and the monomials xq−2. This result motivated the study of Carlitz rank of f, which is defined in 2009 to be the minimum number of inversions xq−2, needed to obtain f, by E. Aksoy et al. We give a survey of results obtained so far on natural questions related to this concept and indicate a variety of applications, which emerged recently.
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