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Mathematical study proves a lower bound for non-monochromatic simplices in triangulated simplices, addressing an open problem posed by Mirzakhani and Vondrák.
Motivated by an open problem in the literature stated by Mirzakhani and Vondrák, we give a lower bound of the number of non-monochromatic simplices for Sperner labelings of the vertices of a triangulation of a given k-simplex with vertices of integer coordinates. This triangulation maximizes the number of simplices over all the triangulations of the k-simplex with vertices of integer coordinates.
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Pascual et al. (2026) studied this question.
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