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il indique que la méthode explicite utilisée dans [Vin05] ne peut être étendue au cas des p-extensions pour p ? 5. Cependant il est déjà positif d'avoir une bonne raison de ne pas se lancer dans des calculs complexes et sans espoir. Par ailleurs, la caractérisation qui est donnée des partitions satisfaisant la propriété ci-dessus a attiré l, Z.L ,
ils reformulent ce résultat en termes de multiset sur un corps fini (et généralisent à tous les corps finis), en donnent une nouvelle preuve beaucoup plus combinatoire, basée sur le Combinatorial Nullstellensatz d'Alon ([Alo99]), le réinterprètent en termes de multisets des valeurs d'un polynôme sur un corps finis, d'arrangements d'hyperplans (ce que j'annonçais vouloir faire à la fin de la première section de l'article ci-dessous, et le relient à la conjecture de Snevily ([Sne99]) ,
a n } et {b 1 , . . . , b n } d'éléments de G de même cardinal n, il existe une permutation ? telle que les produits a i b ?(i) soient tous distincts. C'est dans la version prouvée par Alon dans [Alo00], où G est d'ordre premier et l'un des ensembles peut être remplacé par un multiset ,
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