Abstract
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.
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Vallejo, E. (2007). Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals. In: Herman, G.T., Kuba, A. (eds) Advances in Discrete Tomography and Its Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4543-4_5
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DOI: https://doi.org/10.1007/978-0-8176-4543-4_5
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