Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals
Ernesto Vallejo · Birkhäuser Boston eBooks · 2008
In this chapter we deal with the question of when an n -dimensional binary matrix is uniquely determined by its 1-marginals and with the related notion of (0, 1)-additivity. We present a survey of known results; several of them have been considered before only in dimensions 2 and 3. Here, we show how to extend them to any dimension. The main results are characterizations of uniqueness and (0,1) additivity: one, of algebraic nature, involves matrices with integer entries; the other, of geometric nature, uses transportation polytopes and permutohedra. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.