Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals

  • E. Vallejo
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.


Symmetric Group Binary Matrix Plane Partition Additive Matrice Dominance Order 
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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • E. Vallejo
    • 1
  1. 1.Instituto de Matemáticas, Unidad Morelia, UNAMMichoaconMexico

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