Around Sperner's lemma

2014/05/29 by Oleg R. Musin, Musin, Oleg R · 3 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1405.7513

openalex publication_date 2014/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a generalization of the classic Sperner lemma. This lemma states that every Sperner coloring of a triangulation of a simplex contains a fully colored simplex. We found a weaker assumption than Sperner's coloring. It is also shown that the main theorem implies Tucker's lemma and some other theorems.

Citations

• Kakutani type Borsuk-Ulam theorem

Cited by

• Computing the Hopf invariant
• Minimal simplicial spherical mappings with a given degree
• A Proof of Atanassov's Conjecture and Other Generalizations of Sperner's Lemma

Related

• Meunier Conjecture
• Sperner's colorings and optimal partitioning of the simplex
• Homotopy groups and quantitative Sperner-type lemma
• On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation
• Proving Tucker's Lemma with a Volume Argument