TY - JOUR
T1 - Minimal non-orientable matroids of rank three
AU - Hiraishi, Hidefumi
AU - Moriyama, Sonoko
N1 - Publisher Copyright:
© 2015 Elsevier Ltd.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.ejc.2015.03.025
DO - 10.1016/j.ejc.2015.03.025
M3 - Article
AN - SCOPUS:84933678702
VL - 50
SP - 123
EP - 137
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
ER -