Sperner Theory

  • Zaifu Yang
Part of the Theory and Decision Library book series (TDLC, volume 21)


Sperner lemma [1928] is probably one of the most elegant and fundamental results in combinatorial topology. As we have seen, this lemma provides a very important geometric background for developing simplicial methods. Recall this lemma states that given a simplicial subdivision of the unit simplex S n and a labeling function L from the set of vertices of simplices of the simplicial subdivision into the set I n , there exists a completely labeled simplex, if x i = 0 implies that L(x)≠ i for any vertex xS n .


Unit Simplex Proper Face Label Rule Combinatorial Topology Simplicial Subdivision 
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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Zaifu Yang
    • 1
  1. 1.Yokohama National UniversityJapan

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