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An analogue of Vosper's theorem for extension fields
- Source :
- Math. Proc. Cambridge Phil. Soc., Math. Proc. Cambridge Phil. Soc., 2017, ⟨10.1017/S0305004117000044⟩, Recercat. Dipósit de la Recerca de Catalunya, instname, UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC)
- Publication Year :
- 2017
-
Abstract
- 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 $\dim_FST =\dim_F S+\dim_F T-1,$ when $\dim_F S, \dim_F T\ge 2$ and $\dim_F ST\le [L:F]-2$.<br />33 pages
- Subjects :
- FOS: Computer and information sciences
Combinatorial analysis
General Mathematics
Computer Science - Information Theory
Dimension (graph theory)
Structure (category theory)
Combinatòria
0102 computer and information sciences
Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC]
01 natural sciences
Linear span
Prime (order theory)
Combinatorics
60 Probability theory and stochastic processes::60C05 Combinatorial probability [Classificació AMS]
FOS: Mathematics
Matemàtiques i estadística::Probabilitat [Àrees temàtiques de la UPC]
Mathematics - Combinatorics
Number Theory (math.NT)
0101 mathematics
ComputingMilieux_MISCELLANEOUS
Physics
Mathematics - Number Theory
Information Theory (cs.IT)
010102 general mathematics
Linear subspace
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
11P70 (Primary) 94B65 12F99 (Secondary)
Finite field
Combinacions (Matemàtica)
010201 computation theory & mathematics
Field extension
Combinatorial probabilities
Combinatorics (math.CO)
05 Combinatorics::05C Graph theory [Classificació AMS]
Vector space
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Math. Proc. Cambridge Phil. Soc., Math. Proc. Cambridge Phil. Soc., 2017, ⟨10.1017/S0305004117000044⟩, Recercat. Dipósit de la Recerca de Catalunya, instname, UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC)
- Accession number :
- edsair.doi.dedup.....95dd4dce0a9f93f291a9b60b87ad14ac