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 Bxk 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 B0k 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.

Giovanni Falcone, & Marco Pavone (2021). Permutations of zero-sumsets in a finite vector space. FORUM MATHEMATICUM, 33(2), 349-359 [10.1515/forum-2019-0228].

Permutations of zero-sumsets in a finite vector space

Giovanni Falcone
;
Marco Pavone
2021

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 Bxk 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 B0k 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.
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
Giovanni Falcone, & Marco Pavone (2021). Permutations of zero-sumsets in a finite vector space. FORUM MATHEMATICUM, 33(2), 349-359 [10.1515/forum-2019-0228].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/470670
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