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Sums of Finite Sets

In: Number Theory: New York Seminar 1991–1995

Author

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  • Imre Z. Ruzsa

    (Rutgers University, DIMACS, Hill Center
    Mathematical Institute of the Hungarian Academy of Sciences)

Abstract

We investigate numerous cardinality questions concerning sums of finite sets. A typical problem looks like the following: if A has n elements, A + B has cn, what can we deduce about A and B? How can we estimate the cardinalities of other sets like A − B and A + B + A? This is in quest of a generalization of Freiman’s famous theorem that describes the structure of those sets A for which A + A is small, to the case of different summands.

Suggested Citation

  • Imre Z. Ruzsa, 1996. "Sums of Finite Sets," Springer Books, in: David V. Chudnovsky & Gregory V. Chudnovsky & Melvyn B. Nathanson (ed.), Number Theory: New York Seminar 1991–1995, chapter 21, pages 281-293, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2418-1_21
    DOI: 10.1007/978-1-4612-2418-1_21
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