@techreport{21c51445984c44669e6a6f90b5a3d59f,

title = "Balanced Simplices on Polytopes",

abstract = "The well known Sperner lemma states that in a simplicial subdivision of a simplex with a properly labeled boundary there is a completely labeled simplex. We present two combinatorial theorems on polytopes which generalize Sperner's lemma.Using balanced simplices, a generalized concept of completely labeled simplices, a uni ed existence result of balanced simplices in any simplicial subdivision of a polytope is given.This theorem implies the well-known lemmas of Sperner, Scarf, Shapley, and Garcia as well as some other results as special cases.A second theorem which imposes no restrictions on the integer labeling rule is established; this theorem implies several results of Freund.",

keywords = "econometrics",

author = "C. Eaves and {van der Laan}, G. and A.J.J. Talman and Z.F. Yang",

note = "Pagination: 19",

year = "1996",

language = "English",

volume = "1996-25",

series = "CentER Discussion Paper",

publisher = "Operations research",

type = "WorkingPaper",

institution = "Operations research",

}