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Title:
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Revisiting Kneser’s theorem for field extensions
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Author:
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Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-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 |
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Rights:
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Document type:
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Article - Submitted version
Article |
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