Abstract
Minimal non-orientable matroids have been investigated as a threshold between orientability and non-orientability. The Fano matroid and the MacLane matroid are well-known minimal non-orientable matroids of rank 3. A natural question is whether there exists a minimal non-orientable matroid of every rank r with m elements. In this paper, we give an answer to the question in rank 3 that for every m≥. 7, there exists a minimal non-orientable matroid of rank 3 with m elements. To prove this statement, we construct two new infinite families of minimal non-orientable matroids of rank 3. Furthermore we also investigate representability of the two infinite families.
| Original language | English |
|---|---|
| Pages (from-to) | 123-137 |
| Number of pages | 15 |
| Journal | European Journal of Combinatorics |
| Volume | 50 |
| DOIs | |
| Publication status | Published - 2015 Nov 1 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
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Cite this
Hiraishi, H., & Moriyama, S. (2015). Minimal non-orientable matroids of rank three. European Journal of Combinatorics, 50, 123-137. https://doi.org/10.1016/j.ejc.2015.03.025