Realizability of Polytopes as a Low Rank Matrix Completion Problem

Details Realizability of Polytopes as a Low Rank Matrix Completion Problem Realizability of Polytopes as a Low Rank Matrix Completion Problem

2010-12-16

arxiv.org/abs/1012.3905v2

Mathematics

Combinatorics

Scientific paper

Here we show that the problem of realizing a polytope with specified combinatorics is equivalent to a low rank matrix completion problem. This is comparable to known results reducing realizability to solving systems of multinomial equations and inequalities, but the conditions we give here are more simply stated. We see how this matrix is related to a matrix appearing in a similar result by D\'iaz.

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