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| HAL: hal-00618241, version 1 |
| arXiv: 1109.0134 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2011-09-01) | v2 (2012-04-14) |
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| Plünnecke and Kneser type theorems for dimension estimates |
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| Cédric Lecouvey 1 |
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| (2011-09-01) |
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| 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 Plünnecke 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 Plünnecke 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. |
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| 1: | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| Subject | : | Mathematics/Combinatorics |
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| Division ring – Kneser's theorem – Plünnecke-Ruzsa's inequalities |
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| hal-00618241, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00618241 | |
| oai:hal.archives-ouvertes.fr:hal-00618241 | |
| From: Cédric Lecouvey | |
| Submitted on: Thursday, 1 September 2011 10:58:19 | |
| Updated on: Thursday, 1 September 2011 11:17:44 | |
