Name
Abstract | ||
|---|---|---|
A subset S of N n = {1, 2,…, N} n is a discrete set of uniqueness if it is the only subset of N n with projections P 1 ,…, P n , where P i ( j ) = |{( x 1 ,…, x n ) ϵ S : x i = j }|. Also, S is additive if there are real valued functions z.hfl; 1 ,…, z.hfl; n on N such that, for all ( x 1 ,…, x n ) ϵ N n , ( x 1 ,…, x n ) ϵ S ⇔ ∑ i z.hfl; i ( x i ) ⩾ 0. Sets of uniqueness and additive sets are characterized by the absence of certain configurations in the lattice N 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 n ⩾ 3, there are sets of uniqueness that are not additive. |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1016/0012-365X(91)90106-C | Discrete Mathematics |
Keywords | DocType | Volume |
axes ii discrete case | Journal | 91 |
Issue | ISSN | Citations |
2 | Discrete Mathematics | 21 |
PageRank | References | Authors |
3.32 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| P. C. Fishburn | 1 | 315 | 151.23 |
| J. C. Lagarias | 2 | 563 | 235.61 |
| J. A. Reeds | 3 | 86 | 11.93 |
| L. A. Shepp | 4 | 44 | 18.02 |