论文信息 - Partitions and Sums and Products - Two Counterexamples

Partitions and Sums and Products - Two Counterexamples

Abstract A negative answer is provided to a question of Erdos. Specifically, a two celled partition of N is provided with the property that neither cell includes an infinite set together with all finite products and pairwise sums from that set. Also, a seven celled partition of N is provided with the property that no cell includes an infinite set together with all pairwise products and pairwise sums from that set.

Neil Hindman

[1] Neil Hindman. Partitions and sums and products of integers , 1979 .

[2] Neil Hindman,et al. Finite Sums from Sequences Within Cells of a Partition of N , 1974, J. Comb. Theory, Ser. A.

[3] P. Erdös. Problems and results on combinatorial number theory III , 1977 .