In this paper, we investigate representations of sets of integers as subset sums of other sets of minimal size, achieving results on the nature of the representing set as well as providing several reformulations of the problem. We apply one of these reformulations to prove a conjecture and extend a
Additive representations of real-valued functions on subsets of product sets
β Scribed by Peter C. Fishburn
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 383 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0022-2496
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π SIMILAR VOLUMES
We show that every matrix valued generalized Nevanlinna function can be represented w a u-resolvent of a certain selfadjoint relation acting in a Pontryagin space. The negative index of this Pontryagin space may be larger than the number of negative squares of the given function. The minimal index
+ 1 and no more than for all i. Moreover, these bounds cannot "t be improved. Identical bounds for the spanning number ' f :i no:mal product of graphs are also obtained. . Let S be a collection of subsets of a set X such that their union is X. Define c(X;S), the covering number of X wi;h rLhspect