Sperner labellings: A combinatorial approach
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In 2002, De Loera, Peterson and Su proved the following conjecture of Atanassov: let T be a triangulation of a d-dimensional polytope P with n vertices v1, v2,...,vn; label the vertices of T by 1, 2,..., n in such a way that a vertex of T belonging to the interior of a face F of P can only be labelled by j if vj is on F; then there are at least n - d simplices labelled with d + 1 different labels. We prove a generalisation of this theorem which refines this lower bound and which is valid for a larger class of objects.
[1] Günter M. Ziegler,et al. Hilbert Bases, Unimodular Triangulations, and Binary Covers of Rational Polyhedral Cones , 1999, Discret. Comput. Geom..
[2] G. Ziegler. Lectures on Polytopes , 1994 .
[3] James R. Munkres,et al. Elements of algebraic topology , 1984 .
[4] Jesús A. De Loera,et al. A Polytopal Generalization of Sperner's Lemma , 2002, J. Comb. Theory A.