1. Permutations of zero-sumsets in a finite vector space.
- Author
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Falcone, Giovanni and Pavone, Marco
- Subjects
- *
VECTOR spaces , *FINITE fields , *PERMUTATION groups , *FINITE, The , *PERMUTATIONS - Abstract
In this paper, we consider a finite-dimensional vector space 𝒫 over the Galois field GF(p), with p being an odd prime, and the family ℬkx of all k-sets of elements of 𝒫 summing up to a given element x. The main result of the paper is the characterization, for x = 0, of the permutations of 𝒫 inducing permutations of ℬk0 as the invertible linear mappings of the vector space 𝒫 if p does not divide k, and as the invertible affinities of the affine space 𝒫 if p divides k. The same question is answered also in the case where the elements of the k-sets are required to be all nonzero, and, in fact, the two cases prove to be intrinsically inseparable. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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