Abstract
The aim of this paper is to prove a general version of Plünnecke’s inequality. Namely, assume that for finite sets A, B 1 ,…,B k we have information on the size of the sumsets A+Bi 1+…+Bi l for all choices of indices i 1,…,i l . Then we prove the existence of a non-empty subset X of A such that we have good control’ over the size of the sumset X+B 1+…+B k . As an application of this result we generalize an inequality of [1] concerning the submultiplicativity of cardinalities of sumsets.
Supported by Hungarian National Foundation for Scientific Research (OTKA), Grants No. T 43631, T 43623, T 49693.
Supported by Hungarian National Foundation for Scientific Research (OTKA), Grants No. PF-64061, T-049301, T-047276
Supported by Hungarian National Foundation for Scientific Research (OTKA), Grants No. T 43623, T 42750, K 61908.
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References
K. Gyarmati, M. Matolcsi and I. Z. Ruzsa, A superadditivity and submultiplicativity property for cardinalities of sumsets, Combinatorica, to appear (also arXiv:0707.2707v1).
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© 2008 János Bolyai Mathematical Society and Springer-Verlag
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Gyarmati, K., Matolcsi, M., Ruzsa, I.Z. (2008). Plünnecke’s Inequality for Different Summands. In: Grötschel, M., Katona, G.O.H., Sági, G. (eds) Building Bridges. Bolyai Society Mathematical Studies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85221-6_10
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DOI: https://doi.org/10.1007/978-3-540-85221-6_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85218-6
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