Ordinal sum-sets

Zuckerman, Martin M.

doi:10.1090/S0002-9939-1972-0314626-X

Ordinal sum-sets
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Proc. Amer. Math. Soc. 35 (1972), 242-248 Request permission

Abstract:

A finite set, B, of ordinals will be called a sum-set if there are nonzero ordinals ${\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}$ such that the set of sums of ${\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}$, in all n! permutations of the summands, is B. Let ${B_k}$ denote an arbitrary k-element sum-set; we consider various matters related to the set of numbers n for which there are n summands for ${B_k}$.

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