### Abstract

Language | English |
---|---|

Pages | 181-190 |

Number of pages | 10 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 5 |

Issue number | 1 |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

- matroid theory
- unimodal conjecture
- rank 2 matroids
- rank 3 matroids

### Cite this

*Discrete Mathematics and Theoretical Computer Science*,

*5*(1), 181-190.

}

*Discrete Mathematics and Theoretical Computer Science*, vol. 5, no. 1, pp. 181-190.

**On a unimodality conjecture in matroid theory.** / Dukes, W.M.B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a unimodality conjecture in matroid theory

AU - Dukes, W.M.B.

PY - 2002

Y1 - 2002

N2 - A certain unimodal conjecture in matroid theory states the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r=⌊ n/2 ⌋. We show that this conjecture holds up to r=3 by constructing a map from a class of rank-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.

AB - A certain unimodal conjecture in matroid theory states the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r=⌊ n/2 ⌋. We show that this conjecture holds up to r=3 by constructing a map from a class of rank-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.

KW - matroid theory

KW - unimodal conjecture

KW - rank 2 matroids

KW - rank 3 matroids

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/167/494

M3 - Article

VL - 5

SP - 181

EP - 190

JO - Discrete Mathematics and Theoretical Computer Science

T2 - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1365-8050

IS - 1

ER -