Abstract
For finite sets of integers A 1,…,A n we study the cardinality of the n-fold sumset A 1+…+ A n compared to those of (n−1)-fold sumsets A 1+…+A i−1+A i+1+…+A n . We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets.
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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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Gyarmati, K., Matolcsi, M. & Ruzsa, I.Z. A superadditivity and submultiplicativity property for cardinalities of sumsets. Combinatorica 30, 163–174 (2010). https://doi.org/10.1007/s00493-010-2413-6
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DOI: https://doi.org/10.1007/s00493-010-2413-6