论文信息 - New proofs of Plünnecke-type estimates for product sets in groups

New proofs of Plünnecke-type estimates for product sets in groups

We present a new method to bound the cardinality of product sets in groups and give three applications. A new and unexpectedly short proof of the Plünnecke-Ruzsa sumset inequalities for commutative groups. A new proof of a theorem of Tao on triple products, which generalises these inequalities when no assumption on commutativity is made. A further generalisation of the Plünnecke-Ruzsa inequalities in general groups.

Giorgis Petridis | G. Petridis

[1] H. Helfgott. Growth and generation in $\mathrm{SL}_2(\mathbb{Z}/p \mathbb{Z})$ , 2008 .

[2] Giorgis Petridis,et al. Upper Bounds on the Cardinality of Higher Sumsets , 2011, 1101.5001.

[3] Terence Tao,et al. Additive combinatorics , 2007, Cambridge studies in advanced mathematics.

[4] Terence Tao. Product set estimates for non-commutative groups , 2008, Comb..

[5] Andrew Granville,et al. An introduction to additive combinatorics , 2007 .

[6] Imre Z. Ruzsa,et al. An analog of Freiman's theorem in groups , 1993 .

[7] Imre Ruzsa. Cardinality questions about sumsets , 2007 .

[8] Noga Alon,et al. An Application of Graph Theory to Additive Number Theory , 1985, Eur. J. Comb..

[9] Helmut Plünnecke,et al. Eine zahlentheoretische Anwendung der Graphentheorie. , 1970 .

[10] Imre Z. Ruzsa. Towards A Noncommutative Plünnecke-Type Inequality , 2010 .

[11] J. L. Malouf. On a Theorem of Plünnecke Concerning the Sum of A Basis and A Set of Positive Density , 1995 .

[12] Alfred Geroldinger,et al. Combinatorial Number Theory and Additive Group Theory , 2009 .