Extremal Set Theory: Sperner's Theorem | Probabilistic Methods in Combinatorics | Mathematics | MIT OpenCourseWare
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SOLVED: Section 6.1: Sperner's Lemma in Dimension 3 (a) Consider a tetrahedron T and some subdivision into smaller tetrahedra in the 3-dimensional space, such that each small tetrahedron lies on a face of the big tetrahedron or another small tetrahedron. Let us label the vertices of the small tetrahedra as 1, 2, 3, and 4, in such a way that vertex A1 gets label i, the edge A1A2 only contains vertices labeled i and j, and the face A1A2A3 has only labels i, j, and k. Prove that there exists
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