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Bibliographic Details
Main Authors:	Calvo, L. Á., Merchán, S., Raboso, D., Rodrigo, J., Rodríguez, J. S.
Format:	Preprint
Published:	2025
Subjects:	Combinatorics
Online Access:	https://arxiv.org/abs/2506.05581
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Table of Contents:

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.