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arXiv · 2506.05581

On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation

L. Á. Calvo·S. Merchán·D. Raboso·J. Rodrigo·J. S. Rodríguez
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Abstract

Attending to 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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L. Á. Calvo, S. Merchán, D. Raboso, J. Rodrigo, J. S. Rodríguez. 2025-06-05. On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation. https://arxiv.org/abs/2506.05581

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