An analogue of Vosper's theorem for extension fields
We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/115387 |
| Acceso en línea: | https://hdl.handle.net/2117/115387 https://dx.doi.org/10.1017/S0305004117000044 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial analysis Combinatorial probabilities Combinatòria Combinacions (Matemàtica) Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::60 Probability theory and stochastic processes::60C05 Combinatorial probability Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat |
| Sumario: | We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}$$ \dim_FST =\dim_F S+\dim_F T-1, $$\end{linenomath} when dim FS, dim FT ¿ 2 and dim FST ¿ [L : F] - 2. |
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