### Abstract

A linear extension [x_{1}<x_{2}<...<x_{t}] of a finite ordered set P=(P, <) is super greedy if it can be obtained using the following procedure: Choose x_{1} to be a minimal element of P; suppose x_{1},..., x_{i} have been chosen; define p(x) to be the largest j≤i such that x_{j}<x if such a j exists and 0 otherwise; choose x_{i+1} to be a minimal element of P-{x_{1},..., x_{i}} which maximizes p. Every finite ordered set P can be represented as the intersection of a family of super greedy linear extensions, called a super greedy realizer of P. The super greedy dimension of P is the minimum cardinality of a super greedy realizer of P. Best possible upper bounds for the super greedy dimension of P are derived in terms of |P-A| and width (P-A), where A is a maximal antichain.

Original language | English (US) |
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Pages (from-to) | 293-311 |

Number of pages | 19 |

Journal | Order |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1987 |

Externally published | Yes |

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### Keywords

- AMS subject classifications (1980): 06A05
- Ordered sets
- linear extensions
- super greedy dimensions

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics

### Cite this

*Order*,

*4*(3), 293-311. https://doi.org/10.1007/BF00337892