A simplicial complex is uniquely determined by its set of discrete Morse functions
classification
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complexconnecteddetermineddiscretefunctionsmorsesimplicialuniquely
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We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex of rooted forests of a connected graph G completely determines G.
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