Sets uniquely determined by projections on axes II Discrete case
✍ Scribed by P.C. Fishburn; J.C. Lagarias; J.A. Reeds; L.A. Shepp
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 698 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
A subset S of N" = { 1,2, . , N}" is a discrete set of uniqueness if it is the only subset of N" with projections P,, , P,, where Pi(i) = I{(x,, , xn) ES: xi = j}l. Also, S is additive if there are real valued functions fr, . . , f, on N such that, for all (x1, . , x,) EN", (x1,. . 1 X") E s @ C&.(x;) 2 0.
Sets of uniqueness and additive sets are characterized by the absence of certain configurations in the lattice N". The characterization shows that every additive set is a set of uniqueness. If n = 2, every set of uniqueness is also additive. However, when II 3 3, there are sets of uniqueness that are not additive.