On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915330424569856 |
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| author | Calvo, L. Á. Merchán, S. Raboso, D. Rodrigo, J. Rodríguez, J. S. |
| author_facet | Calvo, L. Á. Merchán, S. Raboso, D. Rodrigo, J. Rodríguez, J. S. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation Calvo, L. Á. Merchán, S. Raboso, D. Rodrigo, J. Rodríguez, J. S. Combinatorics 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. |
| title | On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.05581 |