### Abstract

Let L be a join-distributive lattice with length n and width(JiL) ≤ k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.

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

Pages (from-to) | 155-162 |

Number of pages | 8 |

Journal | Algebra Universalis |

Volume | 72 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 1 2014 |

### Fingerprint

### Keywords

- antimatroid
- convex geometry
- diamond-free lattice
- join-distributive lattice
- permutation
- semimodular lattice
- trajectory

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Algebra Universalis*,

*72*(2), 155-162. https://doi.org/10.1007/s00012-014-0295-y

**Note on the description of join-distributive lattices by permutations.** / Adaricheva, Kira; Czédli, Gábor.

Research output: Contribution to journal › Article

*Algebra Universalis*, vol. 72, no. 2, pp. 155-162. https://doi.org/10.1007/s00012-014-0295-y

}

TY - JOUR

T1 - Note on the description of join-distributive lattices by permutations

AU - Adaricheva, Kira

AU - Czédli, Gábor

PY - 2014/10/1

Y1 - 2014/10/1

N2 - Let L be a join-distributive lattice with length n and width(JiL) ≤ k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.

AB - Let L be a join-distributive lattice with length n and width(JiL) ≤ k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.

KW - antimatroid

KW - convex geometry

KW - diamond-free lattice

KW - join-distributive lattice

KW - permutation

KW - semimodular lattice

KW - trajectory

UR - http://www.scopus.com/inward/record.url?scp=84908129663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908129663&partnerID=8YFLogxK

U2 - 10.1007/s00012-014-0295-y

DO - 10.1007/s00012-014-0295-y

M3 - Article

VL - 72

SP - 155

EP - 162

JO - Algebra Universalis

JF - Algebra Universalis

SN - 0002-5240

IS - 2

ER -