### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 19 |

Volume | 1996-25 |

Publication status | Published - 1996 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 1996-25 |

### Fingerprint

### Keywords

- econometrics

### Cite this

*Balanced Simplices on Polytopes*. (CentER Discussion Paper; Vol. 1996-25). Tilburg: Operations research.

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**Balanced Simplices on Polytopes.** / Eaves, C.; van der Laan, G.; Talman, A.J.J.; Yang, Z.F.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Balanced Simplices on Polytopes

AU - Eaves, C.

AU - van der Laan, G.

AU - Talman, A.J.J.

AU - Yang, Z.F.

N1 - Pagination: 19

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - econometrics

M3 - Discussion paper

VL - 1996-25

T3 - CentER Discussion Paper

BT - Balanced Simplices on Polytopes

PB - Operations research

CY - Tilburg

ER -