Asuresum is a pair (A, n),A ⊂ {1, ...,n−1}, so that wheneverA is 2-colored some monochromatic set sums ton. A “finite basis” for the suresum (A, n) with |A| ≦c is proven to exist. Forc fixed, it is shown that no suresum (A, n) exist ifn is a sufficiently large prime. Generalizations tor-colorations,r>2, are discussed.

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  1. [1]

    P. Erdős, On the representation of large integers as sums of distinct summands taken from a fixed set,Acta Arith. 7 (1962), 345–354.

    MathSciNet  Google Scholar 

  2. [2]

    J. Folkman, On the representation of integers as sums of distinct terms from a fixed sequence,Canad. J. Math. 18 (1966), 643–655.

    MATH  MathSciNet  Google Scholar 

  3. [3]

    J. E. Graver, A survey of the maximum depth problem for indecomposible exact covers,in: Infinite and Finite Sets (A. Hajnalet. al., eds.),Colloq. Math. Soc. János Bolyai 10, North-Holland 1975, Vol. II, 731–744.

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Spencer, J. Suresums. Combinatorica 1, 203–208 (1981).

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AMS subject classification (1980)

  • 05 C 15