2026-04-17T23:19:24Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1140802026-01-15T05:09:23Zcom_2072_1033col_2072_452950

Revisiting Kneser’s theorem for field extensions Bachoc, Christine Serra Albó, Oriol Zemor, Gilles Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres Partitions (Mathematics) Field theory (Physics) Additive combinatorics linear versions Particions (Matemàtica) Teoria de camps (física) Classificació AMS::11 Number theory::11P Additive number theory; partitions Classificació AMS::12 Field theory and polynomials::12F Field extensions A Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the non-separable case, thus solving Hou’s conjecture. This result is a consequence of a strengthening of Hou et al.’s theorem that is inspired by an addition theorem of Balandraud and is obtained by combinatorial methods transposed and adapted to the extension field setting. Peer Reviewed Postprint (author's final draft) 2017-05-31 Article Bachoc, C., Serra, O., Zemor, G. Revisiting Kneser’s theorem for field extensions. "Combinatorica", 31 Maig 2017. 0209-9683 https://hdl.handle.net/2117/114080 10.1007/s00493-016-3529-0 eng https://link.springer.com/article/10.1007%2Fs00493-016-3529-0 Open Access application/pdf