Abstract
We relax the assumption of commutativity in certain Plünnecke-type inequalities.
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References
J. L. Malouf, On a theorem of Plünnecke concerning the sum of a basis and a set of positive density, J. Number Theory, 54.
M. B. Nathanson, Additive number theory: Inverse problems and the geometry of sumsets, Springer, 1996.
H. Plünnecke, Eine zahlentheoretische Anwendung der Graphtheorie, J. Reine Angew. Math., 243 (1970), 171–183.
I. Z. Ruzsa, On the cardinality of A+A and A-A, Combinatorics (Keszthely 1976), Coll. Math. Soc. J. Bolyai, vol. 18, North-Holland-Bolyai Társulat, Budapest, 1978, pp. 933–938.
I. Z. Ruzsa, An application of graph theory to additive number theory, Scientia, Ser. A, 3 (1989), 97–109.
I. Z. Ruzsa, Addendum to: An application of graph theory to additive number theory, Scientia, Ser. A, 4 (1990/91), 93–94.
I. Z. Ruzsa, Cardinality questions about sumsets, Additive Combinatorics (Providence, RI, USA) (A. Granville, M. B. Nathanson, and J. Solymosi, eds.), CRM Proceedings and Lecture Notes, vol. 43, American Math. Soc, 2007, pp. 195–205.
I. Z. Ruzsa, Sumsets and structure, Combinatorial number theory and additive group theory, Advanced courses in mathematics, CRM Barcelona, Birkhäuser, Basel-Boston-Berlin, 2009, pp. 87–210.
I. Z. Ruzsa and S. Turjányi, A note on additive bases of integers, Publ. Math. Debrecen, 32 (1985), 101–104.
T. Tao, Product set estimates for non-commutative groups, arXiv:math/0601431v2.
T. Tao and V. H. Vu, Additive combinatorics, Cambridge University Press, Cambridge, 2006.
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© 2010 János Bolyai Mathematical Society and Springer-Verlag
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Ruzsa, I.Z. (2010). Towards A Noncommutative Plünnecke-Type Inequality. In: Bárány, I., Solymosi, J., Sági, G. (eds) An Irregular Mind. Bolyai Society Mathematical Studies, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14444-8_17
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DOI: https://doi.org/10.1007/978-3-642-14444-8_17
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