Pl\"unnecke and Kneser type theorems for dimension estimates
Combinatorics
2013-08-27 v3
Abstract
Given a division ring K containing the field k in its center and A,B two finite subsets of K\{0}, we give some analogues of Pl\"unnecke and Kneser theorems for the dimension of the k-linear span of the Minkowski product AB in terms of the dimensions of the k-linear spans of A and B. These Pl\"unnecke type estimates are then generalized to the case of associative algebras. We also obtain an analogue in the context of division rings of a theorem by Tao classifying the sets of small doubling in a group.
Cite
@article{arxiv.1109.0134,
title = {Pl\"unnecke and Kneser type theorems for dimension estimates},
author = {Cédric Lecouvey},
journal= {arXiv preprint arXiv:1109.0134},
year = {2013}
}
Comments
21 pages