Revisiting Kneser’s Theorem for Field Extensions
| Autor: | Gilles Zémor, Christine Bachoc, Oriol Serra |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Universitat Politècnica de Catalunya [Barcelona] (UPC), Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Additive combinatorics Field theory (Physics) Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis [Àrees temàtiques de la UPC] 11 Number theory::11P Additive number theory [Classificació AMS] Mathematics::Analysis of PDEs Field (mathematics) 12 Field theory and polynomials::12F Field extensions [Classificació AMS] 0102 computer and information sciences 01 natural sciences Separable space Combinatorics 11 Number theory::11P Additive number theory partitions [Classificació AMS] [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] FOS: Mathematics Mathematics - Combinatorics 11P70 Discrete Mathematics and Combinatorics Number Theory (math.NT) 0101 mathematics Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC] ComputingMilieux_MISCELLANEOUS Mathematics Teoria de camps (física) Partitions (Mathematics) Conjecture Mathematics - Number Theory Particions (Matemàtica) 010102 general mathematics [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA] Extension (predicate logic) Addition theorem Computational Mathematics 010201 computation theory & mathematics Field extension partitions linear versions Combinatorics (math.CO) |
| Zdroj: | Combinatorica Combinatorica, Springer Verlag, 2018, 38 (4), pp.759-777 Recercat. Dipósit de la Recerca de Catalunya instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| ISSN: | 0209-9683 1439-6912 |
| Popis: | 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 a transposition to extension fields of an addition theorem of Balandraud. 17 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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