## Total positivity, Grassmannians, and networks (2007)

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by
Alexander Postnikov

Citations: | 36 - 2 self |

### BibTeX

@MISC{Postnikov07totalpositivity,,

author = {Alexander Postnikov},

title = {Total positivity, Grassmannians, and networks},

year = {2007}

}

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### Abstract

The aim of this paper is to discuss a relationship between total positivity and planar directed networks. We show that the inverse boundary problem for these networks is naturally linked with the study of the totally nonnegative Grassmannian. We investigate its cell decomposition, where the cells are the totally nonnegative parts of the matroid strata. The boundary measurements of networks give parametrizations of the cells. We present several different combinatorial descriptions of the cells, study the partial order on