A note on interpolation of permutations of a subset of a finite field (Q2922932)

The authors are interested in the problem of representing partial functions which permute a specified subset \(A\) of a finite field \(\mathbb{F}_q\) where \(q\) is a prime power. The functions obtained act on \(\mathbb{F}_q \setminus A\) either as the identity map or a constant map. The representation provided in Theorem 3.1 correspond to the case that the function acts on \(\mathbb{F}_q \setminus A\) as the identity map. As a corollary of Theorem 3.1 a formula is obtained for the permutation polynomials corresponding to involutions. Theorem 3.4 deals with the case that the partial permutation acts on \(\mathbb{F}_q \setminus A\) as a constant map.